Erm, you are a little way off.
At MAN there is a "dedicated" Club desk now, usually open only in the mornings for the JFK flight. Use it if you can. MAN will give you your MAN-LHR and your LHR-??? BPs and tag your bags through. Priority tags are hit and miss whether they give you them or not (I NEVER get given them wherever I am) but anecdotally they never make any difference apart from making your bag more liable to get nicked.
After you arrive at LHR from MAN you don't need to clear security again. Follow the signs to the FCC, walk the walk, have your BP checked, go down the stairs to the T4 bus, get on the bus, arrive in T4, relax in Spa...
Coming back is a bit different. Follow signs to T1, get on the bus, get off the bus, enter the FCC and show your inbound First BP alongside your outbound LHR-MAN BP, and that gives you access to Fast Track. Clear security, clear immigration, walk the walk back to T1D again, and relax in the Terraces.
There are a few of us who do fly from MAN in First, but not too many!