england-and-wales
PACE Code C, Section 10, issued under the requirements of
Police and Criminal Evidence Act 1984, Section 66, imposes these requirements on an arresting officer:
10.1 A person whom there are grounds to suspect of an offence, must be cautioned before any questions about an offence, or further questions if the answers provide the grounds for suspicion, are put to them if either the suspect’s answers or silence, (i.e. failure or refusal to answer or answer satisfactorily) may be given in evidence to a court in a prosecution.
Also,
10.4 As required by Code G, section 3, a person who is arrested, or further arrested, must also be cautioned unless:
So the answer is No - the caution cannot be omitted when arresting a person, except as provided in the cases specified by the "unless":
(a) it is impracticable to do so by reason of their condition or
behaviour at the time;
(b) they have already been cautioned immediately prior to arrest as in
paragraph 10.1.
Addendum
The standard form of the caution, in Code G, is
“You do not have to say anything. But it may harm your defence if you
do not mention when questioned something which you later rely on in
Court. Anything you do say may be given in evidence.”
or
“Does dim rhaid i chi ddweud dim byd. Ond gall niweidio eich
amddiffyniad os na fyddwch chi’n sôn, wrth gael eich holi, am rywbeth
y byddwch chi’n dibynnu arno nes ymlaen yn y Llys. Gall unrhyw beth yr
ydych yn ei ddweud gael ei roi fel tystiolaeth.”
But the caution given does not need to be word-for-word identical:
Minor deviations from the words of any caution given in accordance with this Code do not constitute a breach of this Code, provided the sense of the relevant caution is preserved.
And the notes to Code G mention that:
4 Nothing in this Code requires a caution to be given or repeated when
informing a person not under arrest they may be prosecuted for an
offence. However, a court will not be able to draw any inferences
under the Criminal Justice and Public Order Act 1994, section 34, if
the person was not cautioned.
5 If it appears a person does not understand the caution, the person
giving it should explain it in their own words.