I would go for option 1. At check-in ask for the connection to be noted and for assistance at LGW should the connection become tight, someone will then meet you at the gate if necessary.
Also ask for a seat as forward as possible due to the connect.
And make sure they tag your luggage as 'Short Connection - Priority' (and pack some hand-luggage!).
The connection will be tight, and Glasgow-LGW is not a very reliable route. I would consider getting the earlier BA flight which arrives into LGW at 11.00am.
Nick