sorry, but BA are operating within their published rules on this. You have to check-in 45 minutes before the flight. This is available on their website http://www.britishairways.com/travel/chkopt/public/en_c

Unlike US airlines, European ones do not normally allow transfer between flights without charge. In this circumstance, I think you will have to rely on your travel insurance (you did have some didn't you??) to claim that the first flight failed to deliver you on time for your next flight. However with a 1hr40 connection at LHR, including immigration, baggage collection and change of terminal, your travel insurance may well consider that you left insufficient time for the connection.

added: just found the MCT is 1 hour 45 minutes. MCT T4 to T5 - and this applies for a journey on the same ticket, not having to collect baggage. So your travel insurance will probably not pay up