I have permanently imported rifles from the EU to the UK, and temporarily exported from the UK to the EU.
It is effectively impossible to move rifles at the moment. I have a Mannlicher Schöenauer in .458 Winchester Magnum which has been marooned in France for the last 18 months, and goodness knows when I am going to get it. The problem is a combination of the EU tightening firearms restrictions and increasing bureaucracy (in order to prevent excitable Muslims getting their mitts on rifles) and Chinese flu travel restrictions. Even the French - who used to be far more level-headed than the British - have gone completely mad on the issue, but then they have suffered terribly from the over-excited adherents of Allah.
I would recommend Harry Gordon -
https://www.highwoodclassicarms.co.uk/export.htm - as the person to deal with. He his also Holt's recommended shipper, but he is going to cost you. I expect, though, that he will tell you exactly the same as me. Off the top of my head, I think you are probably looking at around £750+ for his services.
Holts will generally store any purchased rifle and - the last time I checked - did not charge for storage.
The best way of getting your rifle will almost certainly be to do it yourself. Add the serial number of your purchase on to your Belgian firearms certificate (for when you import it). You will then have to travel to the middle of nowhere, or Norfolk as we call it, where Mr. Holt lives in his hobbit-hole, to pick it up. I have dealt with the UK customs on this issue previously, and they were surprisingly helpful and efficient. You will need to work through this form:
https://www.gov.uk/government/publications/open-general-transhipment-licence-sporting-guns . If you plan to bring the rifle back on a ferry, declare it to the customs but not to the ferry personnel as they might case problems - either demanding that you lock it up in their ship's locker or - worst case - refusing you carriage.
Just as an aside, in the old days I added the serial numbers to my British and EU firearms passes and that was enough to be handed a rifle and to buy ammunition. With Brexit, we British are no longer allowed to use the EU firearms pass, so the simple route is out.
As another aside, I found that when travelling with firearms between EU countries the customs officers generally had the attitude that as long as the paperwork was correct there was no issue. There was a general assumption that, as a firearms owner, you had already jumped through the hoops and they did not need to - for example - search through your car and sniff your dirty underpants. I never had any problem with the customs and my various rifles.
Don't forget that you will now have to pay VAT on any rifle that you import, as a result of Brexit.
I should make two points absolutely clear: firstly, I am sure that it would be possible for you to pick up and export a rifle, either personally or through Mr. Gordon, but it is going to cost you. If you do it yourself, there is unlikely to be any cost saving once you add in the costs of your time and travel and aggro. Secondly, the EU bureaucrats are making it more and more difficult to own and transport rifles, and particularly to buy in one country and export to another. I had been toying with the idea of setting up a business buying rifles in Europe to sell in the UK, but the difficulty and cost of dealing with the bureaucracy meant that I very quickly gave up on the idea; it would simply have been uneconomical.
Finally, I am not an expert on the subject, so this is general advice only and I do not accept any responsibility if you have any problems.