As TBS has mentioned, British Airways will not check your bags in at Manchester all the way through to, I assume, SEL. Asiana are, however, likely to check your bags in at SEL all the way through to MAN. British Airways are really picky when it comes to doing this.

A 2h 15m connection from T4 to T1 is plenty really. So long as everything goes to schedule. When you clear immigration at T4, follow signs for Heathrow Express. This will take you, free of charge, to Terminal 1.

To try and get Asiana to check you all the way through to MAN though - aswell as your bags. If they do this and give you a boarding card, just follow the FLIGHT CONNECTIONS signs after immigration and you will find a coach to drive you over the airfield (or under it, atleast) to T1 for your next flight.