Yes. Don't lease either. Maybe paying cash, no part-ex, and perhaps ordering FSD gets you allocation sooner [I'm doubttul on FSD. Might have made a difference originally, back in June]. Skip the tow-hook, and white seats.
I ordered an M3 the moment that UK orders opened (I did not have a prior deposit). I ordered FSD, White (which at the time was £1,000 extra), and turned out to be an unpopular colour, but Tesla made lots, and coupled with Heathrow-Handover I got the car in the first shipment, back in June.
I ordered a replacement MS and took delivery last November. From memory that was less than a month start-to-finish. By then they had the Model-3 Group Training PowerPoint Preseation Up and Running ... and that was all I got for the MS ... (as a former MS owner I didn't need anything, but I doubt a Newbie would have been impressed !)
Picked up an M3 a few days ago, (White again, Heathrow again), that was 1 day under a month from ordering.
But ... Heathrow is 100 - 200 cars a day, straight-off-car-transporter-wash-and-handover. If it needs some snagging-fettling you will have to be very lucky to get it done there-and-then, and whilst a come-back-latter appointment will sort it, that might be a month .. or even two
There aren't many Superchargers stalls there, and they are blinking tight to manoeuvre into, and someone else who rocks up wanting Service is very likely to block you in for 5 minutes just as you want to leave ... (my first M3 was charged to 50% or so, this one was charged to 90%, so pot-luck on that).
... but there is a big Supercharger at Heathrow Hilton, and they give Tesla owners a discount - so if you need some grub that's a better solution.
The Provinces are much more likely to give you love and attention.
If you are buying something for teh first time, and it isn't an M3, maybe skip Heathrow.
I think the PowerpPoint is fine, and someone else sat watching may well ask the question that you never thought to ... but Group PowerPoint may not be everyone's bag.