In some ways yes, eating out will probably be cheaper than in London, but I agree with gecko2 re the rent, it's very expensive, I don't know how that compares to London, probably about the same if you are looking at what Gibraltar terms as 'Luxury Property' I have seen studios (i.e one room)in one of the more modern, luxury Apartment blocks between £800 and £1000 a month, so think anything from £800 - £4,000 a month for anything larger.
Cigarettes and Spirits are definitely cheaper in Gibraltar but there isn't much else, the hype about Duty Free Electricals is just hype!, these items may be Duty Free but they will still be more expensive than in the UK or buying on-line and if you need a new Mobile, buy one before you get here as there is little choice and what is available is over-priced.
Morrisons, the only Supermarket in Gibraltar, is expensive compared to the UK Morrisons and very rarely has the BOGOF offers.
Gibralatar isn't very good for Men's clothing, there is an M&S, Next,(both franchises, so higher than UK prices) Peacocks and about 3 other independant stores selling Men's clothes, in other words, not much choice and expensive.
The Buses to get around Gib are cheap, 60p single or 90p return to/from anywhere on the Rock.
Taxis are expensive considering the lower than UK petrol prices.