Was expat on both location so I can share my experience. (5 years in London and 3 years and counting in Singapore. 20 in Malaysia before that)
Nothing beats culture in London when you have the best museums and tourist destination in the world. Although there has been a huge surge of investment in the cultural aspect of Singapore. A lot more investment on the entertainment side and bringing in shows to keep Singapore happy and culturally invested. It's a top destination in Asia, however it will come as a cost. My preferences would still be London on this one. I do miss the weekend to the natural history museum. Huge multi racial community and a mix of nationality makes Singapore diverse, so it's a welcoming place. However it is a conservative country by nature so things like LGBT community is present but suppressed. There are some racism even though people don't admit it, but it's usually not too serious. I give more points to London on this one.
Food and drinks
It's great and one of the most open and easiest to integrate for an expat in South East Asia. Food is affordable and in abundance, you'll find that people here really love their food. Great food can be found at hawker centres (local food court) at a low price but you can also find most international cuisines else where. One thing London has access to its great variety of cheese, wine, European cuisine in the grocery stores (Tesco, Waitrose, Sainsbury's, etc) you can still buy them here in Singapore but most of these ingredients do come at a higher cost. Singapore have heavy tax on alcohol so normal beers are comparible to London's even after conversion. Pub crawls are better in London but club scene and raves are pretty insane over here.
Singapore kill it by a long shot. I don't miss this TFL tube strike and the nightmare commuting to work. In the island (SG), everything is effective and transport time are mostly accurate to the minute. Everywhere is accessible by public transport either by MRT (train) or busses or taxis. Local startup Grab has been waging war with Uber here so lots of great deal for consumers. London has awesome flight and train link to Europe but Singapore has great link to Asia. The latter is usually cheaper as travel destination is great when you're stacking the Singapore dollar against other currencies.
I do miss the Hyde Park and Greenwich a lot but not the weather. Singapore being on the equator means you get humidity, rain, and sun. The first is the killer but once you get pass it, it's great. East coast park is comparible to Hyde Park if not better because of the government funding that goes into them. Around the national stadium, the Singapore government invest huge amount of money into it, turning the area into a giant sports hub. You get free access to tons of facility like running track, basketball courts, indoor arenas... some you pay (small amount) there are tons to do outdoor but it just takes a little more effort to find them.
Living and Driving
Same as London, the biggest cost here is property. Space is a much higher commodity in Singapore so don't expect huge living space unless you are prepared to pay for it or travel. The little red dot does have one of the most efficient public transport so the government actively discourage driving. One way to do it is make driving an insanely expensive investment. Think 3-5x the amount you pay for a car as you would in London. Not much reason to drive in both cities anyway unless you're used to life in Greater London and beyond.
I left this last because it really depends what you do. However you do pay way less tax in Singapore. As a citizen outside of the EU (or now U.K.), I don't miss paying national insurance which I don't get access to most benefits other than the limited NHS. Being the financial hub is south east Asia, Singapore has the opportunity to offer the best pay around. More so if you are in the financial sector. Tech and startup community is still growing but lots of investment coming in to the area, if you have stong skill set and experience to back, there's no shortage of jobs in the tech scene. However don't expect it to be as mature as London. I'm in the tech scene and comparing to London, I can actually live off my income while supporting my wife comfortably.
Ask around and do visit Singapore to see it for yourself. Experience may differ but it's really up to you on what you are looking for.