I can address this somewhat, as I know people who work carbon emissions reporting, although I personally don’t. Apologies for length but I think this is relevant.
Basically yes, economic growth is strongly correlated with emissions growth and so, if GDP goes down following Brexit, UK production (as in CO2 generating activities on UK territory) emissions will decrease, as possibly will UK consumption emissions (the CO2 embodied in things we buy from other countries) however see below.
However, the flip side of lower GDP leading to lower emissions, is that many in the sustainability sector believe Brexit, in general, and no deal Brexit in particular is based on a deregulatory agenda. Deregulation has the strong potential to increase UK production emissions because of lower environmental standards. So, the potential for more things like Druridge Bay open cast coal mining; lower emissions standards for factories etc. Government position is that it won’t happen, but we all know laws can be repealed and as soon as environmental protection is reframed as a ‘choke on growth’ then they likely will be. Greater Crested Newt protection will be one of the first to go, I think, developers have hated that one for years, so we can treat that as a bellwether for the current claims that there will be no reduction in environmental standards.
Further, whatever form of Brexit we get, we will be buying more goods from outside of the EU. The EU generally has world leading environmental standards (which does not mean perfect) so consumption emissions are likely to go up. For example we end up buying more goods from eg China, or the US both of which still have significant coal powered electricity generation, then consumption emissions for these goods (made with coal powered electricity) will be much worse than if we bought the same goods from eg France which doesn’t. Not to mention goods have to be transported for thousands of miles rather than hundreds increasing the CO2 emissions from transport.
Leaving the EU also removes the UK’s membership of the EU as a negotiating block at the Conference of Parties where global ambition on climate change is set. The EU, although far from perfect, is a leader on action on climate change globally, and the UK outside of it is a far less powerful voice and has much less influence on outcomes.
In addition, a no deal Brexit (and maybe other forms of Brexit, who knows?) removes UK scientists’ eligibility for EU research funding, which is a significant part of the national research budget. It means less research can be done to address climate change and will also lead to a brain drain as scientists move elsewhere (this is already underway).
And to conclude on that cheery note, I don’t know anyone in the UK sustainability sector who is pro-Brexit or thinks it will be good for either the UK environment domestically or decrease UK CO2 emissions, any possible short-term dip notwithstanding. Apart from anything else, government is going to be tied up for decades in renegotiating all the trade deals its undone, so the political will and funding for tackling climate change just won’t be there.