Having just done this a few times - Google Maps always routed me through Heathrow Express as the fastest option. Typically 1 hour from London Bridge area to Terminal 5.

From MK: take train to Euston, walk to Euston Sq, take Circle/Met/Hammersmith & City to Paddington and onto Heathrow Express.

If it's running through by the time of your trip then I'd just get on Elizabeth Line from Euston, probably via Northern Line to Tottenham Court Road.

Or, if you really want to squeeze the price, hop off at Hatton Cross, go through the barrier, and straight back again to avoid the TfL Heathrow permanent peak surcharge. £3.40 off-peak, £5 peak, then the Hatton Cross to Heathrow bit is free on contactless.

It's the Heathrow version of the East Croydon trick going to Gatwick.

Heathrow Central
 

This station gets you to T2 and T3 with free onward travel to T4 or T5.

I really don't see very many people doing this - especially with luggage/ It seems to be more in the theoretical FT world of things to do than in the real world.

I did MK to LHR quite a few times in the past and never took the train. National Express runs several direct services from MK coach station, relatively cheap tickets if booked in advance, journey takes roughly 2 hours, there are only a couple of stops (LTN and Hemel Hempstead or LTN only for certain services) before reaching LHR T2/3/5. Of course one should take the traffic into consideration when considering this option, M1/M25 are notoriously bad. As for the other option (i.e. Watford) which had been previously suggested, I think it is worth mentioning that this is a local bus service (starting in Hertford/Welwyn Garden City/Hatfield or somewhere else in Hertfordshire) and can get crowded at times.

G

I’m looking at these options currently.
Walk to Euston Square (5minutes), . Tube to Paddington, Elizabeth Line (every 30 mins) to Heathrow T5. £12.80

or

Tube to Heathrow T5 £5.50

That's the inertia TfL is relying on, along with passengers just not knowing.

I've done far sillier things in my time, and - particularly coming back when I have plenty of time - I might as well wait on the platform at Hatton Cross for five minutes at most and save money than do exactly the same on a mainline station concourse.

Besides which, I'm belligerent enough to want to stick it to TfL for making just one station in their entire network permanently peak, particularly when the bulk of the track has been in place since 1977 and the trains haven't seen improvement for years either :).

The OP may also want to watch out for weekend engineering works on that stretch of the Piccadilly Line. Last time I tried to use it on a Sunday, the line was closed and the only offered TfL option was the Liz line - at full cost rather than Underground pricing, of course.

I got on the 423 bus, which meets the Liz line at Feltham station, and still caught my mainline train ...

When the Piccadilly line is closed they often lay on replacement buses non-stop from Heathrow to Hammersmith, which IMO is an improvement on the tube, and "free" too

I did it when I was on a T4 train but heading to T2. Saved a few pennies, got my steps up a little and took no extra time. All courtesy of FT