If you have 6 hours in LHR then I'd be tempted to get the Lateral Flow test done in Halo (£15) or ExpressTest (£30) while in T5. But you can do it the day before in Manchester if you prefer. At check-in, if you show the LHR test booking email, they will allow you to fly to LHR, and through check luggage, but won't issue the LHR boarding pass with the ADOC flag. If you want to use VeriFLY then you don't have much choice but to do the test in Manchester.