Hi Rosemary
If you are flying straight from Heathrow, you will be allowed to check in two bags, each weighing up to 23kg - so you could check in both your main suitcase and the soft-sided holdall.
However, if you are taking a flight from a regional airport to connect with the main flight (eg Newcastle - Heathrow - Kenya) you will be limited to the regional airline's limit, which is likely to be one bag weighing 20kg. To get around this, you would need to put your soft-sided holdall inside your main case and take it out when you get to Kenya.
But either way, you won't need to drag any bags around Heathrow.
I hope this makes sense. Let me know if not!
Kind regards,
Olly, your editor