And the North Yorkshire MP can certainly be forgiven for wanting to get on with it, as he played a key role in getting the difficult process to this late stage as an Assistant Whip.
Reflecting on an unprecedented period in British political history, he tells The Yorkshire Post: “It’s dominated so much over the last couple of years and I can’t wait for it to be over and for us to be out of the European Union, so that we can get on with doing what we were elected to do.
“And that’s to try and make the lives of constituents better.”
Although he no longer formally takes part in the whipping operation, Adams is proud of the role he has played in implementing the referendum result.
“It’s fascinating and you do feel a sense of being part of history,” he says.
“I do have a signed copy of the EU Withdrawal Bill on my downstairs loo wall… Hopefully my grandchildren will understand why that is there.”
But getting to that point wasn’t easy, given the Conservatives’ poor 2017 election result which left them with a minority government, dependent on Northern Irish DUP MPs to get them over the line in key votes.
In such circumstances, the Whips office becomes central to the functioning of Government, with every vote crucial to delivering legislation.
“As a whip it’s been an amazing couple of years since the vote,” Adams reflects.
“And since 2017, since we haven’t had a majority to get the EU Withdrawal Bill was a huge victory and a great success, given the parliamentary arithmetic.”
But he also reveals that it causes frustration among MPs over the amount of time they are forced to be in Westminster, poised to enter the voting lobbies.
He says: “You have to be much tougher on your flock in terms of them being available to vote at the correct time. The opportunities for MPs to go and do constituency events diminishes.
“If you have a huge majority like Tony Blair had, his MPs could be in their constituencies most of the week and just turn up for votes when they were needed...
“That doesn’t happen, especially if you are a Northern MP.”
The frustrations look set to continue with the second meaningful Brexit vote expected next week, and no sign yet that there is close to a parliamentary majority for the Prime Minister’s deal.
Should it be voted down again, MPs will then get the chance to vote for a no-deal Brexit or a delay to the process.
For Adams, as with many Tory backbenchers that Mrs May must win over, it is the Northern Irish backstop aspect of the agreement, which could tie the UK into a customs union with the EU, that is the “sticking point”.
“There needs to be real change in that,” he says.
“We don’t want a situation where part of the UK is treated differently from the rest of it and we are locked into a customs union arrangement.
“The Government made it very clear in their pamphlet before the referendum that leaving the EU meant leaving the customs union, meant leaving the single market - everybody was told about that.
“There can be no doubt in any MP’s mind that that is what the vote to leave meant.
“It’s a pity that there are those members of parliament that don’t quite understand how democracy works.”
He adds: “If it hasn’t changed it’s going to be very difficult for many MPs to vote for it. Because the previous deal was defeated so heavily, then to get this deal over the line it has to change.”
But while his analysis on how the vote can be won stands, there has so far been little movement from EU leaders that suggest a deal can be struck before the 29 March exit date.
With the deadlock making no-deal more likely the warnings about the impact it could have on the UK economy have been getting increasingly alarming, with reports of possible food and medicine shortages and the army said to be on standby in the event of civil unrest.
However, Adams insists that the option of leaving without an agreement should remain on the table while negotiations are ongoing.
“I certainly won’t be voting to take no deal off the table,” he says.
“I think an extension, unless it is a very determined, defined period for clearing up legislation, that is understandable, but again you can’t have a situation where this thing rumbles on and on because people just want to try to scupper it.
“I’ve been in business for 20-odd years before I became a Member of Parliament and I never went in to any negotiations saying: ‘before we start I’d just like to tell you, I’ll pay you whatever price you want. I’ll take delivery whenever you want to deliver it, it’s up to you to draft the terms and conditions.’
“That isn’t how you should do business and that isn’t how we should conduct these negotiations.”
He adds: “Exiting without a deal will be very difficult for Britain and there will be short-term challenges, very much so.
“However, it is doable in the medium and long term. It is better than not leaving.
“There’s more risk, I think, if we don’t honour the result of the referendum.”