You'd have to have some amazing microclimate to get away with it. Most citrus aren't hardy below 7 to 10 C.
You can, however, do mediterrean-style plants that are more hardy. Olives are a bit tougher - once established, they're normally OK down to -10 or thereabouts. So if you're not somewhere really, really cold, you might well get away with them outside! (My brother-in-law has one in his Coventry garden). Figs also will grow, and may even fruit if grown in a warm and sheltered spot and given the right kind of care. Obviously herbs like sage, rosemary etc. are fine too. Bay trees too can get really quite large in the UK too - my Dad has one that's nearly as high as his house!
Then there are also lots of hardy palms like the Mediterranean fan palm, and things like hardy yuccas. There are a whole range of less authentically Mediterranean plants that would add to that 'exotic' look too! Things like Choisya ternata, which is Mexican, crocosmia (African) etc.
Add a few terracotta pots and some bright splashes of colour (and a large prosecco) and you could still imagine you're in Italy!
I bought a lovely lemon tree in Aldi last year. It survived the winter in a pop-up greenhouse, but hasn't flowered. I'll probably get rid of it. St Monty of Don moves his citrus trees into a greenhouse for the winter.
My olive tree (which came free with a pot I bought on eBay) has not only flowered but produced teeny olives. It has survived outside on the patio all year and I love it.
Holly is quite right - there are lots of options for Mediterranean-style planting.
I have a book on growing fruit and vegetables in Scotland specifically and they recommend a variety of lemon called "Meyer's Lemon" as being relatively hardy. They also recommend bringing them inside for all of winter - till June, basically. I plan to get one and put it by our patio doors in winter.
So if it's possible to grow lemons in Scotland I'm sure it can be done further south.
They do say that oranges can't be grown here, though.