desemirates - I connect T1 > T4 frequently so have been both ways:
If your bag is NOT through checked then pick it up, leave T1 via Heathrow Express and check in at T4. Move smartly as this takes a while and especially security at T4 as I recall the only time I did it. Since UL is not a oneworld carrier it's not impossible that this is how it will work.
If your checked bag *is* through checked and you are not given a boarding pass then follow this advice from
www.heathrowairport.com
From the BAA Heathrow website:
Connecting from Terminal 1 UK & Ireland to Terminal 4
Your connection will take approximately 60 minutes, from landing to departure gate. From Terminal 1, head for the Flight Connections Centre. Show your ticket and visit our airline desks before making your way by coach to Terminal 4's departure gate.