Oh thank you everyone 
No need for pool - the whole thing was 90min from first contraction to birth. I basically must have had a "silent" first stage of labour, as I was lying in bed with DH shortly after midnight, feeling some "pelvic pressure" - which I now realise was contractions
- and then I felt like I'd suddenly wee'd myself uncontrollably, which of course was waters going.
I felt really chilled and rang the home birth MW to let her know, and she said to relax and get some kip. So we went to the other bedroom and tried to go to sleep, but within about 20min I was having really painful "pelvic pressure" and realised I wouldn't be able to sleep. I got up to pace corridor and within minutes it was just unbearable - I was throwing up, more waters were coming, there was blood, but also really bad pain. I stopped being able to keep silent and realised they were proper contractions, at which point DH pointed out that there wasn't much more than a minute between them - he'd been timing based on my moans. I suddenly started feeling I couldn't cope with just hypno breathing and so DH rang the now again and she said she'd come.
It was probably only 30-40 min or less but it just got worse and worse - I was clinging to the door jamb of our bedroom and telling DH that if this was the early part of labour, I wanted to go to hospital and have an epidural! Of course, in hindsight it was actually transition. Then I suddenly felt a massive uncontrollable spasm down below as though I was going to have a really big poo
and I told DH I needed to push. Thankfully after a couple of contractions with the pushing feeling the MW arrived. She tried to get me on the bed to examine me but I just fell onto my hands and knees - it was the only bearable position - and she knelt down to examine me from behind and said there's a head
about two pushes later I could feel her head being born, which was a huge relief, and then her shoulders came with one more.
Second degree tear which they stitched with gas and air and that was
literally the only pain relief I had bar some local anaesthetic and some paracetamol after it was all over.
Phew! The MW said it was super fast for a first timer and I should have future babies at home.....but I think we'll park that idea for the time being!!