There are all sorts of things wrong with the typical Leaver's impression of the £39 billion.
A) It's not a "payment to get a deal" i.e. we're not buying ourselves a future arrangement. It's money we already committed to spending, both in terms of future EU budget we still have to pay (just like you may have to keep paying for a while if you want to get out of a phone or broadband contract, because there's a minimum contract period), and in terms of related costs that we created and therefore are responsible for (e.g. the pensions for past UK MEPs and functionaries in Brussels). The EU also took into account the value of our share of the EU's total assets (e.g. government buildings, etc.) that we won't be using any more when we're not EU members, and deducted that from the total to arrive at the £39 billion.
B) Legally it is possible that we might be able to walk away from paying, though it would cause an almighty row that would burn on for years. However, that would pretty much guarantee nobody - neither the EU, nor other potential future partners - would be willing to sign a decent trade deal with us? Why? Because we'd have proven to them we were unreliable and not to be trusted.
Putting it into everyday terms, would you go into business with somebody who very publicly blew off their debts to their previous business and walked away? Not because they were bankrupt, but just because they didn't particularly feel like paying them. I thought not.
C) The money isn't due as a lump sum. We're not trundling a convoy of trucks stuffed with £50 notes to Brussels. Instead, it's due in decreasing amounts over the next 40-50 years (yes, really - we're still due to be paying some of it in the 2060s). So that makes any suggestion that the same money would be available to spend as a big juicy Brexit dividend instead utter nonsense, because there was never a £39 billion lump-sum at all.
D) Tim Martin is an astute businessman who runs a very large chain of pubs with a decent degree of success. That doesn't mean he knows anything about the WTO (he doesn't) or the intricacies of international trade and trade agreements (he doesn't), or tariffs (he doesn't), or the needs of the industrial sector and just-in-time production (he doesn't) or the specific legal consequences of a no-deal Brexit (he doesn't). His skillset doesn't map onto Brexit, much like a brain surgeon might be an absolutely diabolical plumber.
Unfortunately, what his own narrow business success has given him is a soapbox, and plenty of money to slosh around to amplify his mistaken and/or misleading Brexit information. It must be nice to be able to afford to print new leaflets every week with your favourite anti-EU rants in them, regardless of the fact that very little if any of what they say is factual or true.