With that kind of baggage, forget Ryanair. In addition to the standard baggage fee, they will charge you an excess baggage fee of £15 per kg above 15kg.

Easyjet is feasible: their checked baggage allowance is 20kg and, importantly, their carry-on allowance is limited by size but not weight. By juggling things a bit, you might be able to keep within the allowance.

BA will allow you one bag with a maximum weight of 23kg of checked baggage on domestic and European flights. Not sure whether they would bother to charge if you are at 25kg. If they do, they will charge a flat fee of £25.

Most other legacy carriers will allow, as Aviatrix said, 20kg. Policy on excess baggage varies from one to the other.

Another thing to bear in mind is that not all European carriers have reasonable one-way fares. UK airlines (BA and BD) do and a number of European airlines also have such fares to and from the UK but quite a few are still pricing on the antiquated model of a minimum stay/sat. night stay (AF and KL spring to mind here).

If you are going to hop around in Europe, it may well be worth your while considering buying a pass of some sort (afaik, all three main alliances have Europe pass-type products if you fly with one airline in the alliance across the pond). Do your home work and compare to the cost of flights on your planned itinerary and see which works best for you.