Flying between AMS and London is cheaper typically than Eurostar. You can go proper cheap and try easyJet to LGW or STN or LTN (I think they fly to all three), but risk with all the seating and bags it will end up more than KLM. Although one-way will be expensive with KL...

Flying AMS-LCY is well faster than the train, even the direct one.

If you can't take the direct train because it's not running, you can either take a late train from Brussels and get to Brussels with an early train (either Eurostar, former Thalys, or NS IC Direct) and make a day of it, or you can do AMS-PAR-LON.

I would suggest doing it in AMS-LON-PAR direction though, with either flying to LON or making a stop in Brussels (it's worth a visit for at least a couple of hours)