Cactus Rescue update - needs identification please anyone ?

  So , back in December 2017 my friend had given me this beautiful cactus . It had belonged to a dear friend of hers who had sadly passed away . It needed to be re-homed and she knew that I loved cacti and would I like to have it ?
  Unfortunately , it had a bit of an accident , as in , a bit of a tumble on the way over to me in the car .  Most of it's roots were completely torn away  . Not one to give up that easily , I re-potted it , in fresh cactus mix compost , a nice new terracotta pot , a handful of sharp grit on top and four pencils to keep it propped up while it re-adjusted and grew new roots .

 As we were going into Winter , I decided not to water it in , so the only moisture was what the fresh cactus compost already had in it .
 It looks to be quite an old cactus and definitely worth saving .
My friend told me that it used to flower every year without fail !

 I placed it on the kitchen windowsill which has a radiator underneath it , to give it a little warmth from below to encourage new roots .
 There it is , with a few other cuttings ( Epiphyllums ) and a Dicksonia antarctica  -Tree Fern looking in through the window for company .

Anyway , it seemed to be doing fine , I removed the pencils and decided to move it upstairs to my South facing bedroom windowsill .
 In the last couple of days it has begun to put out flower buds ...about six of them , and yet another one seems to appears every-time I go to look at it .

 We are  having some beautiful hot and sunny days again here in Mullion on the Lizard in Cornwall ....Saturday , Sunday and Monday all forecast to be very hot .
 This cactus is loving it ! I,ve never had a cactus in flower on this windowsill before . It closes up when the sun goes in, so I expect it will last longer than the Epiphyllums out in the greenhouse which only last a day and a night usually .
  Anyway , I,m just delighted to see this in flower  !
The main body of the cactus has sunken down..I suppose while it was using it's  energy to heal it's self and partly because it was the Winter .You can compare the first pictures with this one . It should expand again during the Summer as and when I begin to water it .
 Please can anyone identify this cactus for me ? I just cant find one like it in any of my books .
  Hope the sun is shining where-ever you are  !

                                  Identification needed please ? Anyone ?