After all, he had many conversations with Paddy Ashdown in the run-up to the 1997 election, which is what led to what was effectively a "non-aggression pact" between the two parties at that time.
However, the Conservative collapse that year gave Blair a landslide victory, and he proceeded to lead a majority Labour government.
Some long-lasting good came from the relationship, not least on constitutional reform. But on the defining issue of Blair’s premiership, Iraq, the Liberal Democrats rightly and vociferously opposed him.
Now, over 20 years later, Blair has come full circle and is once again trying to sow the seeds of collaboration between the two parties.
I admit, I tried to squeeze my views on this into a tweet – but I couldn’t. It’s not as simple as either unconditionally opening your arms to welcome co-operation, or permanently closing the door.
My own approach in Oxford West and Abingdon has been to encourage people to switch to support the Liberal Democrats from all sides. We did this by reaching out to those who agreed with our position on key issues. Some were national, like Brexit and the climate crisis, others were more local, like opposing the Oxford to Cambridge Expressway or campaigning for our local NHS services.
In 2017, the local Green Party stood aside to help me defeat the Conservative MP. Many Labour supporters and moderate Conservatives joined them. This created a progressive alliance of voters, built on support for strong public services, opposing a hard Brexit and putting tribalism aside to defeat the Tories. We overturned a Conservative majority of just under 10,000 votes and took the seat against the odds.
Then last year, alongside a strong local Lib Dem team, we had Greens, Labour members and pro-EU Conservatives campaigning for me. The result was a majority far bigger than we had anticipated. Across the country we saw ground-breaking cooperation between the Lib Dems, Greens and Plaid Cymru, working together in the best interests of the UK. Cooperation can be done, and when done right, can also mean winning.
At the national level, I found it easy to work alongside colleagues from all parties in the People’s Vote campaign. What matters is advancing the issues we care about, not the colour rosette we were wearing.
There have been plenty of other examples of this. Norman Lamb and Luciana Berger (as a Labour MP) worked for years to advance the mental health and social care agendas. After the Welsh Assembly elections in 2016, Lib Dem Kirsty Williams was appointed education minister by Labour’s Carwyn Jones, and she remains in post.
Lib Dem councillors work with colleagues from other parties up and down the UK. What matters is making things better for the people we represent. And here is the thing. Voters like it. It’s a politics that’s about them, not us.
Where cooperation around shared, progressive and internationalist agendas can help make a difference, we should support it.
The Lib Dems also need to start winning again. That means framing our message, rooted in our liberal values, in a way that persuades many more people to vote for us. We’ve done that before, under Paddy and under Charles, and we need to do so again.
We need to rebuild our reputation as the party that is on the side of the majority on investment in high-quality education, support for our NHS, and urgent action on the climate emergency.
There is a massive challenge for whoever is the new Labour leader too. As long as the Labour leadership concentrates on their leftist base, rather than the broader electorate, they are doomed to continual failure.
And Labour needs to focus on their real enemy. Last week I was in Leeds and Sheffield, and I heard far too many stories about thuggish behaviour by Labour activists directed at Lib Dem councillors and activists. "Yellow-Tories," they cry, justifying what have been in some cases arrestable offences. That attitude has to stop.
I gained and held my seat by building a broad coalition of support, based on campaigning on the issues that matter to my constituents. It’s not rocket science. It’s how every Lib Dem who has ever won a parliamentary or council seat has done it.
The Liberal Democrats need to set out to do this nationally and regionally. And I hope those in the Labour Party will encourage reform and steer their comrades towards cooperation, just as the Greens and others have done. Because the priority for anyone in opposition to the Conservatives should be to get back to winning again. Our country’s future depends on it.
Layla Moran is the MP for Oxford West and Abingdon