Obviously, but the relative bargaining positions of the parties are relevant to negotiating a favorable agreement, and is one of the main reasons for forming unions of any sort.
While the UK leaving the EU has made the EU economy meaningfully smaller, our economy is less than a fifth of the size of the EU's today. That impacts our relative bargaining position with other countries.
It can have positives when negotiating with nations that see themselves to be adversarial to the EU - e.g., we got a somewhat better deal with the US than the EU did on tariffs, and perhaps we would be in a preferable position to negotiate with China (although strengthening economic ties with China is fraught for other reasons, and could sour relations with the US). With most countries though, our bargaining position is simply not as strong as the EU's (and is even weaker than it was when we were part of the EU, which is when many existing agreements were negotiated).
When we left the EU, we lost access to existing agreements (including return agreements). Everything we have successfully negotiated since is worse than what we had before.
There's also the inconvenient matter of geography - we're an isolated island, with a dwindling economy, whose closest trading partners are the EU. If we start negotiating deals or taking anti-immigration steps that are adverse to the EU's interests, that could result in the EU - upon whom we are always likely to be economically reliant, taking economic steps against us.
Posters seem to think we could go the Austalian route but that's a fantasy. Austalia is its region's economic powerhouse and most of its trade is with China and the US, who are largely unimpacted by Austalia's policies towards asylum seekers. There's no local trade partner for them to piss off.
Australia also has a geographic advantage. It can intercept boats before they reach its waters, and have a lot of local countries who are heavily reliant on trade with Australia but are largely irrelevant to Austalia's economy. That means Austalia can negotiate offshore processing deals that are likely a fantasy for us.
Yes, there was Rwanda but the UK Supreme Court ruled that plan illegal since Rwanda wasn't deemed a safe country. Farage seems to think that, if we leave the ECHR, that would get around the issue - I don't think so; the court cited other international treaties (like UN ones) in reaching it's decision.
The UK, as a standalone economic powerhouse, has had it's day. Unfortunately, we're now also on the outside of the union that continued to give us outsized relevance, and is always likely to be our major trading partner.
The way to make our already bad situation worse would be to elect Farage or some other government that is antagonistic towards the EU. If any country is going to end up the de facto "51st state", it might well be the UK rather the Canada. For so long as the US is in something of a trade war with Europe, it might prop us up a little - and Farage does seem to recognize that, hence his cozying up.
I do appreciate that there is more to Brexit than economic considerations (a decent chunk of leave voters felt it would be the right thing even if the economic consequences were poor) but I think we ultimately need to accept that our diminished standing on the world stage will have far reaching consequences, and those likely includes our ability to deal with illegal immigration. There is a flip side on immigration, though, in that it does give us the ability to control legal immigration (which is far larger, in raw numbers) than as part of the EU. That's certainty a significant positive to highlight and we absolutely do need to reduce our reliance on high levels of legal immigration, we just haven't yet figured out how to navigate the birth rate issue and its relation to the welfare state (particularly pensions).
(Formerly FairHazelMentor - deleted my account to avoid the temptation of posting and procrastinating but have no willpower...though I suspect my windbaggery is identifiable enough)