Freelance (Ltd Company) UK or BE?

I would remain resident in the U.K. and set up the company there and travel to Belgium as required. Check if there is a limit on days in Belgium. I think you are ok if you are going back and forth and don’t have a fixed residence here. Certainly ten times easier and cheaper and simpler to set up a company in UK.
Of course, as Brexit progresses, all sorts of things can change in the coming months for how you do business, invoice etc. No one knows how it will pan out.

Whether to set up in Belgium of the UK will depend on a whole variety of issues.

e.g. if your company is in Belgium, you'll have to manage VAT (i.e. you'll have to invoice with VAT and file Belgian VAT returns every quarter), whereas if you're in the U.K. you'll be "exporting" your services and therefore not billing VAT (but still filing VAT returns).

Where will you be generating expenses? If mainly in Belgium, then a Belgian company may be better, if mainly in the U.K. then visa versa.

IR35 (not RI35) is also relevant in the U.K. as HMRC is looking very carefully at these types of constructions which are increasingly being refused.

You say that you have (sic) "no obligation to take up residence in either country". If so, where are you based right now, and where are you tax resident?

Setting up a Belgian company will be easy enough, however you will have very significant issues setting up your bank account if you are not resident here.

You will also have problems filing your VAT and tax returns without an eID issued in Belgium, and will therefore have no option but to hire an accountant to do these for you.

And that's just what I can think of between spoonfuls of cornflakes while I'm eating my breakfast.

Get an accountant, sit down, talk through all the issues and then take proper professional advice.

Consult Ernst & Young or KPMG for advice.

Further to my post above, good advice from the two anons. I agree that if you are not resident here with an ID card and a bank account here, it will be difficult to set up a company in Belgium. I set one up 4 years ago and have been resident here for many years. An accountant can set it up easily but all the rules on tax, social security, dividends etc are a nightmare. You also have to prove that you are competent/qualified/certified to run the type of business you are setting up. I had to produce qualifications from 35 years earlier and have them translated and certified!
If you are UK resident it will be a lot easier in U.K.

From the previous comment: "I agree that if you are not resident here with an ID card and a bank account here, it will be difficult to set up a company in Belgium."

I think that it will be impossible! Normally, at least one director needs to be resident in Belgium. Same for bank account; no bank here will accept you. Maybe check an Estonian company using the "E-residency" programme, it might work for you.

And just to follow up on my earlier post;

"Setting up a Belgian company will be easy enough, however you will have very significant issues setting up your bank account if you are not resident here."

The exact same issue arises in the U.K. i.e. It's really easy to set up a U.K. limited company. It takes about 10 minutes and costs £12 at Companies House

https://www.gov.uk/limited-company-formation/register-your-company

However, if you are not tax resident in the U.K., or at least one director isn't resident in the U.K., it will be exceptionally difficult to set up a bank account in the U.K. for your company. So although you'll have a company, you can't accept payments, and within a few months, your company will be closed down by HMRC and Companies House.

We have been looking at the OP setting up his own company.
There are companies like www.avalara.com who set up international tax reporting, especially for eCommerce so that, for example, a Canadian buying and selling in Europe can register for VAT and charge/reclaim it.

Sort your permanent residency out (as that's where you pay tax), and talk to a local accountant about the exact details of your business and how best to operate.

You're clearly utterly clueless about this at the moment and you have an awful lot to learn about and consider.

IR35 will have been in force for 20 years this April, and it's still a nightmare for people who operate PSCs.