A LGW - LHR transfer / missed connection question please.

Delayed 57 mins inbound to LGW and missed LHR to EDI connection resulting in >3hrs delay in arrival at final destination. Original connection allowed 3hrs 20m connection time from LGW to LHR but delay cut that to c.2hrs20m. Not sure on the original reason for the 57min delay (doing some digging) but pending the outcome of that is it worth submitting a claim to BA? Single ticket straight through direct with BA. Full details:

BA2038 MCO - LGW 18 July (57 min delay)
Transfer to LHR
BA1448 LHR-EDI 19th July - missed the flight
Ended up on BA1450 arrival at 23:53 - >8hrs delayed.

So I guess the whole claim will revolve around a) reason for original delay and b) minimum compliance time for LGW/LHR connection (see BA "recommend" 2hrs but even the 2hrs20mins we that simply wasn't doable with baggage collection, transfer, recheck bags etc)