I don't think it's relevant that the OP moved away. I know people always make a huge fuss about one parent "deciding" to move away from the other, but the truth is that the RP often has little choice, especially if they've been living somewhere expensive like London where they can't afford to give the kids a decent life on their own now there's much less money. Often the RP needs to move somewhere cheaper or closer to family to do the best for the children. I don't sense in this case that the OP's ex was lining up to be the "resident parent" if the OP decided to move anyway and leave her son with him (the OP refers to him as being not very "hands on" and her being lonely and still doing most of the parenting on his visits). It doesn't sound like he would have provided much day-to-day support for her and her son even if they'd stayed in London. So she'd be parenting pretty much on her own in an expensive city with no family support. Are people seriously suggesting that he should be allowed to essentially keep her "prisoner" in London, parenting alone and potentially unable to afford a decent lifestyle for her son, when he sounds like quite an uninvolved parent?
There's a reason why the RP is usually allowed to relocate when cases like this go to court...While, all things being equal, it is in children's best interests to have frequent contact with both parents, it is also in their interests to have a decent standard of living and a parent with sufficient social support from friends and family to parent properly, especially where the NRP does not have a history of being particularly involved. Interestingly, the courts are much more willing to refuse permission where the NRP has been an equal "hands-on" parent actively doing half the parenting.
OP, I don't think you're under any obligation to let him stay in your spare room and I think it's bad for you in terms of moving on...However, depending on the age of your child (I don't think you've said how old he is), your ex should be having him for weekends by himself, including overnights unless your son is very very young. Otherwise, he'll never learn to step up and be a proper parent and build a proper relationship with your son. Depending on your financial situation, it would make sense to contribute to flight costs/accommodation if you can afford it to maintain the relationship, but I don't think you're obliged to do so if you can't afford it. That's on the assumption that you're the one mainly responsible for the financial costs of raising your son and your ex is paying minimal child support. If so, you're already doing your share.