Checked bags won't make a bit of difference when you step off that plane and have to re-enter security. In my experiences, it takes ATLEAST one hour, usually more, to clear security at Heathrow.
You are very lucky your connecting flight is within the same terminal. That will save you the hassle of taking the train and having to run literally one mile past the shops and sea of travelers. I have made this mistake before and missed a British Airways flight home direct to Austin Texas.
My advice is to not take any liquids with you through security during re-entry. My mistake was that British Airways hands you bottled water while you wait to step off the first plane. I jammed that water into my bag for later, and didn't even think about it until I was already stopped by Heathrow security for a bag search.
This bag search took over an hour itself (almost two hours!), beyond the normal hour of typical Heathrow security. Even with begging and pleading with senior staff at Heathrow, they still could not expedite anything and I missed my plane by mere seconds, as I watched it leave terminal as I ran up to the gate. Had my flight been within the same terminal, I might have made it. They even performed a "shift change" and new employees came to take over security lines, and that took 20 minutes, with nobody in sight! I almost grabbed my bag and ran...
Please allow for a minimum of one hour, in perfect circumstances, to clear London Heathrow airport. If you have any liquids on you from your previous flight, expect a 3 hour wait and to miss any connecting flights. I have had it happen twice now and I simply refuse to fly through Heathrow anymore because of it.
I am very curious of your experience because I have emailed Heathrow authorities several times about connection times and their massive wait times.