First things first, this isn't a "recommend a good financial advisor" question.
I'm looking for advice on how best to approach the world of assisted personal finance & investing. I'm currently at university in the UK and will be finished soon. I have some cash to play about with and I want to grow its value once I start work.
I have a basic understanding of financial instruments, but I have no experience in markets and trading.
You want a fee-only advisor. He charges like an architect or plumber: by the hour or some other "flat fee". That is his only compensation. He is not paid on commission at all. He is not affiliated with any financial services company of any kind.
His office is Starbucks. He does not have a well lit office like the commission broker down the street.
He does not want you to hand him your money - it stays in the brokerage account of your choice (within reason - some brokerage accounts are terrible and he'll tell you to get out of those). He never asks for the password to your brokerage account.
Edit: The UK recently outlawed commission brokers. These guys were competitive "sales types" who thrive on commissions, and probably went into other sales jobs. So right now, everyone is clamoring for the few proper financial advisors available. High demand is making them expensive. It may not be cost-effective to hire an advisor; you may need to learn it yourself. It's not that hard.
Ever hear of a plumber who works totally for free, and makes his money selling you wildly overpriced pipe? That's what regular "financial advisors" are.
They sell products that are deliberately made unnecessarily complex. The purpose is first, to conceal sales commissions and high internal fees; and second to confuse you, so the financial world feels so daunting that you feel like you need their help just to navigate it. They're trying to fry your brain so you'l just give up and trust them.
Products like whole life and variable annuities are only the poster children for how awful all of their financial products are. These products exist to fleece the consumer without quite breaking the law.
Of course, everyone goes to see them because they have well lit offices in every town, and they're free and easy to deal with.
Don't feel like you need to know everything about finance to invest. You don't need to understand every complex financial product that the brokerage houses bave dreamed up: they are designed to conceal and confuse, as I discuss above, and you don't want them.
The core of it is fairly simple, and that's all you really need to know.
Look at any smaller university and how they manage their endowments. If whole life, annuities and those complex financial "products" actually worked, university endowments would be full of them. But they're not! Endowments are generally made of investments you can understand. Partly because university boards are made of investment bankers who invented those products, and know what a ripoff they are.
Some people refuse to learn anything. They are done with college and refuse to learn anything more. I hope that's not you.
Because you should learn the workings of everything you're investing in.
If you don't understand it, don't buy itl
And a fee-only financial advisor won't ask you to.
1000 well-heeled, well-advised university endowments seek the most successful products on the market... And end up choosing products you can understand. That's good news for you.
If someone recommends a particular investment rather than a class of investments, assume they are getting a commission and walk away.
If someone recommends whole life insurance as an investment vehicle, walk away.
Find someone whose fiduciary responsibility is explicitly to you as their client. That legally obligated them to consider your best interests first. It doesn't guarantee they are good, but it's done protection against their being actively evil.
The other answers are good, but not UK-specific.
You need to look for an Independent Financial Advisor (IFA). These are regulated by the FCA and you pay them a time-based fee for their services, they do not take commission on the products they recommend to you.
The Government Money Advice Service page (hat tip to @AndyT in the comments on the question for the link) tells you how to go about finding one of these and what sort of questions to ask. Contrary to the note in the answer by @Harper, in the UK many IFAs do have perfectly nice offices, this is not a sign that should put you off.
Personal recommendations for IFAs are usually the best way to go but failing that there are directories of them and many will have an initial conversation with you for free to ensure you are aligned with each other.
I think the other answers raise good points. But to your question, "How do I find an honest financial adviser" ask your friends and family. See who they talk to and confide in. Go meet that person, understand what they do and how they view things and if you gel, great. Honesty and strong ethics exist in individuals regardless of laws.
What is it you're trying to accomplish? You just have some money you want to put aside? You want to save for something? You want to start a budget or savings plan? Your first step may be talking to a tax person, not an investment adviser. Sometimes the most significant returns are generated when you simply retain more of your earnings and tax people know how to accomplish that.
You're just graduating university, you're just going to get your first job. You don't need to hunt for the right heavy hitter 30% gains generating financial adviser. You need to establish your financial foundation. Crawl, walk, then run.
There are some basics (that transcend international borders).
If you don't know much about investing, most (if not all) retirement and individual brokerage type accounts will give you access to some kind of market index fund. You don't need to multinationally diversify in to high fee funds because "emerging markets are screaming right now." Typically, over a few years the fees you pay in the more exotic asset classes will eat up the gains you've made compared to a very low fee market index fund.
You can open free accounts at a number of financial institutions. These free accounts at these banks all have a list of zero commission zero load funds, all have something resembling an index fund. You can open your account for free, deposit your money for free, and buy shares in an index fund for free.
Large and well-known companies are typically a good starting point. That doesn't mean that they are the best or even above average good, but at least they don't cheat you and run with your money.
A core point is someone you pay, not the company whose investment he sell you. Although the latter seems cheaper on first glance, it isn't - if you pay him, his interest is to do good work for you; if they pay him, his interest is to sell you the product with the highest payment for him. That does not imply that they are all that way; it's just a risk. There are many good advisers that live from commissions, and still don't recommend you bad investments.
Depending on the amounts, you could also read up a bit and open an account with a online investment company. It is discussable, but I think the cost for an adviser only starts to become worth it if you are deep into 5 digits of money.
If your financial needs aren't complex, and mostly limited to portfolio management, consider looking into the newish thing called robo-advisers (proper term is "Automated investing services").
The difference is that robo-advisers use software to manage portfolios on a large scale, generating big economy of scale and therefore offering a much cheaper services than personal advisor would - and unless your financial needs are extremely complex, the state of the art of scaled up portfolio management is at the point that a human advisor really doesn't give you any value-add (and - as other answers noted - human advisor can easily bring in downsides such as conflict of interest and lack of fiduciary responsibility).
disclaimer: I indirectly derive my living from a company which derives a very small part of their income from a robo-adviser, therefore there's a possible small conflict of interest in my answer
Most individuals do not need a personal financial advisor. If you are soon entering the world of work, your discretionary investments should be focused on index funds that you commit to over the long run. Indeed, the best advice I would give to anyone just starting out would be:
For most average young workers, a financial advisor will just give you some version of the information above, but will change you for it.
I would not recommend a financial advisor as a necessity until you have seriously complicated taxes. Your taxes will not be complicated. Save your money.
