There is plenty of time with a 2h35 layover as you have FastTrack through customs (shouldn't be more than 10 mins), then arrivals lounge is to your right after you exit customs (well signed). Shower+breakfast takes 1h, then take the HEX (heathrow express train) to T1. This is now operating normally once again (thankfully) so you have worst case 7 min travel time+15 min wait time+15 min walk time (yes there is quite a bit of walking involved transferring landside instead of using the airside buses). Leaving you with 45 min to clear security at T1 and get to the boarding gate. Unfortunately you won't have FastTrack for security at T1, which might be a problem depending on the date/time of your flight (may have to cut the shower at T4 short). I've only used FastTrack at T1 departures and that normally takes under 5 min, but I have seen rather long regular lines and believe it could take over 30 minutes worst case. You do have to watch the time and not dawdle but it is possible to do comfortably. For those who have lounge access at T1 (departing in CE or with OW Sapphire status) the better strategy is to transfer airside, skipping the arrivals lounge, and use the showers in the T1 Terraces lounge.