I'm a Londoner and I am happy that you live here in England well away from them but totally understand the feeling of obligation when they visit, that you have to stay in touch and the questions of 'why do you do it to yourself?' coming from your wife and the way that you probably don't have a straight answer as to why you still see them but you could write a long list of reasons not to be in touch with them yet that one unknown unclear reason of why you do keep in touch seems to override all those reasons to cut contact. I know where you are coming from.
You thinking of paying for the taxi from Heathrow is you being normal (and very generous), you being a caring family member - despite the way they have treated you it is not 'natural' for you to stoop to their level and to be cold or cruel towards them. That in itself, whilst it is good for them to take advantage, shows a quality in yourself that you need to acknowledge - you are a good person, better than they will ever be and they do not deserve to be related to someone like you and therefore gievn the treatment and the abuse you really really owe them nothing at all and THEY do not deserve to be in contact with someone like you.
Everytime they visit you, everytime they speak to you on the phone or have an insight into your life they are attempting to creepily keep the control going (something that is unspoken between them and you) but at the same time it is gradually erasing the 'evidence' of the way they have treated you in the past....they can say 'well, we haven't done anything to you..if we had..why would you be speaking to us, letting us stay over at yours?' It is a crafty game. Don't beat yourself up for letting it happen up until now, as I said you are a normal, good person and you have behaved normally. But, you can chose not to play their games anymore as it normalises the way they are...they are not normal and I really do understand that is a lot easier said than done to cut contact, I get that totally.
My dad is abusive and his family are too, I met the whole lot of them when I was 17 they were all abusive in their own ways and tried to make me feel grateful for knowing them but would be emotionally and mentally abusive..my dad is the main narcissist and I woke up to their treatment after many attempts to speak to them and to be nice to them, buy them gifts, think of them often send them things in the post to keep in touch..then I stopped. I realised..then they started saying cruel things about me as if I was 'not normal'. I avoided them, then stupidly got back in contact - they made me apologise for losing touch saying I was 'very English' and cold by 'forgetting them'. Then...I wised up totally and stopped making that effort. My life picked up, I made good friends, started travelling..all those things some of them were influenced by and tried to get a piece of the action but I ignored them...then, I met a nice guy...woah, that is their biggest fear ever! Suddenly the nastiest aunt pathetically commented on my photo 'trés jolie' (very pretty) the other day, why? because she sees that it might be serious with this guy and because in my dad's culture they are so family orientated..they would hate hate hate it if I had my own family one day, separate from them..wow what a threat and even worse, I might tell people about their treatment, shock horror.
Strangely, I'm still in touch with my father (who is constantly cruel) and I don't know why I do it but I do...so I understand your situation in that respect. I'm 23 now and I know this has to stop. You know you have to stop too, but you don't know how to start.
How was the visit? Let us know how it went and whether it has helped you to make a decision as to what to do.