BMI has a low-cost subsididary called bmibaby with a hub in Birmingham. Also fly from other UK airports like Nottingham, Manchester, etc...

Thanks to all for your help. And you are absolutely right about Ryanair not fly the route that I need. It was Easyjet that I had looked into.

I am still concerned about the weight of my baggage, however. How many pounds is 15kg, about 35? There is no way I will be able to pack that lightly.

The extra baggage fee is about 5 Euros per kg (or possibly 5 pounds, depending on the airport).

None of the European carriers have generous allotments on an intra-Europe route. But take a look at the various airline policies to see what would be best and give you the lowest price overall.

Note you can also take a reasonably-priced train plus ferry combination between Amsterdam and London:
http://www.amsterdamexpress.co.uk/
http://www.londonexpress.nl/

1 kg = 2.2 pounds