Hello Pat
I hope that this little bit of info helps to put your mind at rest. When you arrive from Manchester at Terminal 5 Heathrow make your way to the Train Station which is underneath the Terminal. Heathrow Express provide a free transfer to Terminals 1 &3. Station is called Heathrow Central. Please note that Heathrow Express also do a non stop service from Terminal 5 direct to London, so make sure that you are on the right train!!
Heathrow Central is about a 5 minute walk to Terminal 3.
I don't know where you get the energy from to get from Manchester to Beijing in one go. I am going the week before you and I am overnighting in a Heathrow Hotel. I have to make my way to Heathrow from Gatwick via the M25 with National Express. That will be a thrill!!
Best wishes
Peter