Congrats OP! As previous poster suggested, you cannot be entirely sure at this point that it will be a straightforward pregnancy. And if it is, surely a private midwife service is less justifiable? I'd think the main reason for using them is that they may be able to provide certain services that the NHS don't? I guess you'd see the same midwife all the way through and have more freedom with appointments, but the cost can be up to around £5000 for the entire pregnancy for a private midwife; that's a LOT of money before you've even considered everything you need for a baby, and it may not include separate optional additions to your private care.
With some private midwives I'd imagine you'd get more support with things like breastfeeding, labour practice etc and if you've got the money just lying around, there's no reason why you shouldn't pay for it.
But however much people criticise the NHS, I think that even when it goes wrong, they do an amazing job (and for FREE!). As long as you do your own research into pregnancy, labour options, possible things that can go wrong in birth, postnatal care, breastfeeding etc, the NHS is an amazing service.
Would be interested in hearing your reasons to go private OP.