You are entitled to the transfer costs as part of the EC261 regulations.

There is a BA imposed soft limit of £50 for a taxi.... but you could probably dispute that if it costs more.

You could also be entitled to compensation if your new flight is more than 60 minutes prior to the cancelled flight.

See here for further details :-

https://www.flyertalk.com/forum/brit...61-2004-a.html