Having lived in both London and NYC I think there are a lot of things that are cheaper here in the UK, although London is the most expensive place to live here so now that I live outside London I'm not sure I'd ever go back. (I was a student when I was there anyway.)
Your wages do seem to go a little farther here in the UK, although keep in mind I live in one of the home counties now so it'll be cheaper than in the center of London. I earn the same amount per hour that I did back in the US (as in, just change the $ to £) but I am on a zero hour contract. Even though I get good hours they're not guaranteed. Also, full time at my old company was 40 hours, and in my new one it's 37 hours, although with the exchange rate I have the potential to make pretty much exactly the same.
The tube costs more than the subway, but I think it's a *slightly* nicer system. I never had to wait 45 minutes for the tube and I had to wait that much at LEAST when I was commuting on the subway.
Housing is similar but maybe a bit cheaper in London. When I was in London I paid £700 for a room in a 4 bedroom shared house in Zone 2. At the same time (so I don't have to adjust for inflation) my friend in New York was paying $1100 per month for a room in a 3 bedroom shared flat (but with no living room) in Inwood in Manhattan. So I was paying slightly less as the bills were included in my rent and weren't in hers. Right now our energy bills are a lot lower than my family's in the US, but we don't have a clothes dryer and dishwasher, and are generally more careful.
Groceries are a LOT cheaper here. In NY my family of 3 adults would spend at least $150 per week on groceries. This week, our grocery bill was £32 for me and my husband for a similar quality of groceries. We'll spend maaybe £10 more topping up on milk, crumpets, another loaf of bread for lunches, etc throughout the week but that's the most.
Eating out is cheaper in the US in my experience, but drinking is a little cheaper here. Or maybe I'm just used to Manhattan prices.
Health care is a big one. In the US, at LEAST a third of my paycheck would go toward health insurance. I lived with my parents and there is NO way I would have been able to move out on my own while paying for health insurance. I would have been spending almost 40% on health insurance and ALL the rest on rent, leaving nothing for food or transport or anything else. Here we pay NI tax which is a much much smaller percentage of our paychecks, and there are no copays when you go to see an NHS doctor. Some prescriptions are also free, such as birth control pills. (BC is free because of Obamacare in the US, but I remember before that, and mine was kind of expensive.) You can also get free prescriptions if you're of a certain age or have certain conditions, I believe, but even if you don't qualify for the free prescriptions there's a cap on how much they can charge per medication (£8.60, might be free outside England??).
And then there are other things that cost less in the UK but are not mandatory. Theatre tickets are significantly cheaper on the West End than on Broadway, and same goes for regional theatres. Many museums are free, especially (but not limited to) London, while similar ones in NYC cost $20-$30 to visit.
I hope this is helpful. The other thread raised a lot of interesting things although I definitely don't agree with 100% of what was said over there. For example, I find London and New York to be equal levels of stressful.