Well yeah, "should've" (short for "should HAVE") is fine, it's what I usually say, but you sometimes here* (and read) what is unambiguously "should OF" - as Rich says, it's not to do with being "posh" or not, it's just wrong.
Anyway, accents on TV are a funny thing. There's a definite "regional accent code":
Scottish: nothing implies good, Protestant honesty and trustworthiness like a nice well-spoken Scottish accent (I'm guessing it's generally a middle-class Edinburgh accent? sounds like the Scottish equivalent of RP, basically). It's especially handy on adverts for things that are good for your body or, better still, your soul - for heartstring-tugging earnestness, you can't beat a really serious, sober Scottish accent for the v/o for your charity ad featuring abused donkeys or malnourished African children.
Northern: Yorkshire/Northumbria accents (Scouse and Manc, not so much) are de rigeur if you want to imply friendly, salt-of-the-earth matiness. Channel 4 worked this out about ten years ago and have exclusively employed Geordies as their anouncers ever since (all the better to distinguish the channel from the stuffy old BBC, of course). This approach can be taken to a patronising extreme, as in for example Victoria Wood's nauseating "Ooh crikey, Grommit!" Yorkshire brogue used on the Asda ads recently.
Cockney/Essex: Is your advert intended to appeal to BLOKES and LADS???? Then this is the accent for you!
West Country: can be used to impart the flavour of orl fings aaagriculch'ral; very often put on ("Mummerset") and generally played for laughs.
Brummie/Midlands: rarely heard, but, like West Country, generally seen as a 'comedy' accent.
Irish: WELL BEGORRAH, IF OI'M NAT THE MOST LOIKABLE ACCENT IN DA WHOLE WOIDE WORLD! Used to generally excruciating effect to imply, like Scottish and Northern accents, friendliness, honesty etc. etc., though often with an added 'comedy' element. Often works best if spoken very rapidly in a high-pitched, excitable manner.
Joanna Lumley: car insurance.
*christ, I really am a spastic sometimes