There are risks here and reiterating that you’re in a stable relationship doesn’t really address those. Most people think their relationship is stable before they have a baby.
You haven’t answered PPs about whose house it is and whether it is rented or mortgage. I’m going to assume mortgage as you say saving for a bigger place but you haven’t said who the house belongs to. If it’s his, that would explain his reluctance to marry as he’s protecting his asset. If it’s yours, you really need to get advice to protect your asset for your child (and any future children).
I would suggest getting married before TTC because there are some areas of potential problems and marriage adds some protection. You mention that you want to save for a bigger house and a wedding ceremony, you get good maternity pay in a stable civil service job. However, you don’t love your career and want to be a mum, it sounds like you’ll be planning to be a SAHM? In which case, you won’t get great maternity pay, you’ll get SMP and need to pay back any enhanced maternity pay. Then you’ll want to save for a bigger house and a bigger wedding while you’re a SAHM.
If you do continue to work, you have nursery fees whilst saving for a bigger house and a bigger wedding. Please don’t be relying on the universal free hours offer, it’s unsustainable at the current levels, it might be taken off the table after the general election and providers don’t have to provide it (our nursery isn’t). The house will always take priority, especially as you are planning for baby to be in with you. After that, the house will need work. Then the kids activities will start costing money. You’re going to be a long time before you save for a bigger wedding.
Let’s say I’m wrong and you can save for the bigger wedding within the first few years after the baby is born, it’s possible your partner is freelance so he just works more to earn more. Except he’s a freelance lorry driver so he won’t be home if he’s working extra. You’ll be raising a baby alone, your older child and presumably his child too (you’ve painted it as his mother isn’t in the picture). You’re raising 3 kids with no help from your partner, you might be a SAHM or you might be working but your partner will be doing this “for you, to give you the wedding you deserve”. Are you stable enough to survive solo parenting while he works more and more hours?
Even if he doesn’t work more hours and you can both save enough with a baby, you will still be the default parent. Your partner may well be hundreds of miles away when nursery call because your kid is sick (and then spreads it to the other two). He can’t just drop everything at work and come back. It’ll be you who has to drop everything. You say you aren’t that bothered by your career (even though you seem proud you’ve worked hard for it), so maybe the career stagnation won’t bother you, maybe you won’t be bothered by the one who looks like a flake and can’t do a good job. However, there is a chance that this is another area that may cause you to build resentment to your partner.
There is a lot of areas for potential conflict. It doesn’t mean you’re going to split up but you are going to have to work out a way that works for both of you. I don’t think it’s going to be a walk in the park, there will be some conflict. You might feel like calling it quits. Being married might just push you to keep going that bit more because getting a divorce is expensive. It might not but at least you’ll have the legal protections of marriage in place if you do then call it quits.