Our local library hands out a sheet to borrow each session for all the parents to follow along with the kids. Try seeing if they have the handouts or are willing to make a copy for you.
I'm from the states and learned it as Eensy Weensy Spider not Itsy Bitsy.
Hokey Kokey (Hokey Pokey)
Ring a Ring a Roses has different lyrics to the US
You can also do "Round and Round the Garden" on your child's stomach. My kids love it like that.
Grand Old Duke of York is a fun one for kids and great for interaction. If your child's a baby you can lift them up and "drop" them at low, or get your toddler / preschooler to march around and stand up / crouch low to the song.
Here's a good list of Nursery Rhymes and their history in the UK:
http://www.rhymes.org.uk/.
Unfortunately a lot of songs can have various sets of lyrics to fit them, so it's not a precise science. The way my MIL sings "Bicycle Made for Two (Daisy Bell)" is different to anything I've ever seen online. It's possibly just a regional version of how the song was sung.
Hang in there. If anything it gives you a focal point to talk to your child about your childhood. My daughter likes hearing what I was like as a little girl and at the same time my MIL tells her about what her Dad & Aunty (whom she's nearly the spitting image of) were like as children.