Depending on the age of the car, you may fall foul of London’s ULEZ. You should be alright with anything from after 2015, at the moment:
I don’t think that the government will be banning diesels for a while yet, but I’d be surprised if London doesn’t increase the ULEZ standards ahead of the national government.
If you’re mainly doing city-driving then a hybrid still (just) works out cheaper to run, but they are more expensive to buy. An additional point to consider would be that all hybrids are automatics, which may help MrsHYG.
In London you also have the added consideration of parking permits. Each borough council has their own system, but all of them are looking to reduce car-use by reducing resident parking spaces, restricting permit numbers and/or increasing permit costs. Some councils (Waltham Forest, for example), scale their resident permit prices depending on emission levels.