AFAIK, there is no baggage agreement between TAP and BA.

TAP are only required to check your bags through to EDI if you have a through ticket. You may find that the TAP agent is quite happy to do it, but don't expect it.

On the return journey, BA will not check your baggage through unless you have a through ticket. Had TAP been a member of the OneWorld alliance, rather than Star, things would have been different.

Personally, I would plan my trip assuming that TAP will not check your bags through and allow enough time at LHR to collect your bags in T2 and for you to take them over to re-check them with BA in T1 (or T5 if you are travelling after 27 March 2008). Likewise, for the return journey.