Actually there were quite a few things the EU was offering in the trade deal which were similar to before, which the UK declined, if the UK was prepared to subscribe on similar terms as before. These things were in the news in the UK, if you cared to read it, so we kind of saw some of them being rejected by the UK in realtime.
My understanding from the news during the negotations was that something similar to common market access under substantially similar terms was on the table from the EU, as were several variations of it. But these were all rejected, because they were viewed by some _in the UK_ as "too soft, soft Brexit, Brexit in name only". Enough politicans and, how shall we say, "influencers", wanted a "hard Brexit", and that meant something bold, symbolic and rejecting things too similar to what had been in place before (including much that was on the table from the EU).
Many little things were on the table from the EU as well, regardless of the main deal, that were seemingly rejected by the UK for no convincing reason.
The ability for performing artists such as musicians, DJs, etc to do tours of Europe as they did before, for example, was on the table from the EU, but the UK turned it away, because of course we would not want EU citizen artists able to do the same reciprocally. So that wiped out a large part of those UK artists' businesses and lifestyles for no obvious reason.
The Erasmus program, also, which allowed students to travel on exchange programs through many of the countries, swapping with their counterpants coming to the UK.
I think both of those suffered from ideology, because in virtually every speech by Theresa May that I heard with regard to the negotiations when she was PM, one of the most up-front and prominent sentences seemed to be in the prelude over and over: "Freedom of movement will end". It sounded more important than anything else. She has also been the architect of the "hostile environment" too, which is frankly legislated evil and still ruining lives. She was reportedly upset at the Brexit vote initially, but saw immigration control and removal of the UK from the European Court of Human Rights as a silver lining, so everything bolsters my view that it was a major motivation for her.
The famous "oven ready deal" which Boris Johnson said he would get through if he was elected in 2019, won him an election, and then he got it signed and ratified, and then within about 6 months he was already publically committing to breaching the terms. One wonders if the UK gov't ever intended to honour the terms or if it was a bait and switch at the time it was signed.
It's because of how that was done (and still is being) that the UK's access to the Horizon science & technology Europe-wide collaborative R&D funding pool has not been renewed. That too, is something the EU had kept on the table, if the deal treaty was honoued.
That one's a particular shame because the UK was a net beneficiary and had many top quality R&D groups depending on that funding. The UK gov't says it has its own R&D funding pool to replace it, but nobody believes it will really roll out matching anywhere near the previous level, nor with the previous quality of international collaboration.