Hi Op,
UK theme parks are really hot on pointing out the dangers of riding extreme rides whilst pregnant- there are multiple signs up stating that pregnant ladies should not participate.
Obviously, you can't go on rollercoasters/ teacups/ pirate ships etc, due to the strain/ G-force/ pressure that the safety bars and ride movement exert on your bump.
However, you can still enjoy calmer rides like carousels/ big wheels, plus the 4D cinemas/ live shows that a lot of theme park have on offer.
We've had merlin cards several times over the years which have sometimes clashed with my pregnancies. Merlin has a facility which allows you to 'freeze' the annual card until your baby is born/ a little past the newborn stage. Look on the merlin website for details of how to request this.
Also, some theme parks (Drayton Manor definetely) allow you massively reduced entry if you show your pregnancy notes- obviously as you won't be able to partake of all the attractions on offer.
On a plus side, once you've had your littl'un, you are entitled to a parent swap pass at most of the theme parks- this allows your partner to queue as normal/ ride/ then get the pass stamped on exit/ and you can enter the ride via the disabled or fast track exit to enjoy the ride without queueing at all.
We have teens as well as littlies, so normally 3 teens and DP ride together while I wait with littlies, and then when they exit, I re-enter with parent swap pass with a teen in tow (so 1 teen gets to ride twice in 5 mins!), so that I can enjoy the ride with someone rather than riding alone- I think strictly speaking it's only meant to be the parent who didn't get to ride the first time that's allowed back on, but riding by yourself seems rubbish, and staff haven't batted an eyelid in the 3 years we've been doing it our way. Perhaps if you don't have other kids, you can go with another couple?
Good luck, and enjoy your pregnancy