It should be noted that we, our, ourselves aren't generally used with singular meaning. The use of we as a singular is called the "Royal we" because it is sometimes associated with the Queen.
By contrast, however, the use of us as a singular is widespread in colloquial British English, and isn't considered pretentious (if anything, the opposite).
The usage is common enough to be noted in the dictionaries. Cambridge calls it "not standard", while Oxford judges it more kindly as simply "informal".
From Cambridge Advanced Learners' Dictionary:
us pronoun (ME)
UK not standard (especially used in spoken English) me:
Give us a light, mate.
Give us it here and I'll see if I can mend it.
From Oxford Living Dictionaries:
us .... 2 informal first person plural Me.
‘give us a kiss’
The form is noted in the full Oxford English Dictionary as follows:
Eng. regional, Sc., Irish English, and colloq. Chiefly in unemphatic use (frequently with 'give'): me; to me.
Not including a quote from a dialect dictionary, and not including the much older Royal use, the OED's first citation for this usage of "us" is from 1857, when it appeared in the famous novel Tom Brown's School Days:
T. Hughes Tom Brown's School Days i. iv. 92: Tell us something more about the pea-shooting.
"Us" for "me" is also noted as a "commonly" encountered "nonstandard use" by Randolph Quirk et al., A Comprehensive Grammar of the English Language (Longman, 1985).
(In my view, singular "us" is significantly less strongly stigmatised than certain other nonstandard usages, such as "ain't" or the double negative. Nevertheless, I would certainly avoid using singular "us" at a job interview or on any formal occasions or at any time when you're trying to impress someone.)
On the other hand, the use of "let's" in phrases like "let's have a look" (= "let me have a look") is even more widespread, and is not considered nonstandard (because although "let's" stands for "let us", it can be taken as a polite way to make the addressee feel included - and also because "let's" has been partially grammaticalised, so not all speakers equate it with "let us").