Of course not all redemptions will have to go through London. As mentioned by Paulchili, US-Asia will probably go up although we don't know. What we know about US redemptions, however, is that like everything else, they will be charge on a per segment basis. So if you typically fly LGA-ORD, the cost is unlikely to change, however, if you typically fly LGA-DTW via ORD, it is likely to increase as it will now be the cost of two flights. That is, of course, unless BA does an exception for the USA (they have done one for domestic UK connections only so far).

We also don't know how thorough BA will be in applying their distance based logic. We all assume they won't implement it for the US but if they did, of course, everything would change prices and it would increase a lot for transcon flights.