Blair did not realise he would win so easily in 1997. He thought that he might need Lib Dem support, so included the referendum idea as a pre-emptive sweetener to any deal. The long term object seems to have been to form a coalition and then replace the socialists in the Labour Party with Lib Dems, so as to create a New Labour Party. This would reverse the split in the British centre-left, which took place in the early 20th century with the original rise of the Labour Party.

In fact Blair won so big that he could not plausibly offer a coalition to the Lib Dems. He did form a joint committee between Labour and Lib Dem leaders, which did some useful work on constitutional issues but deadlocked on electoral reform for the House of Commons.

To keep the Lib Dems hopeful, Lord Jenkins was asked to do a report on a new electoral system which could be proposed at the putative electoral referendum.

Jenkins produced the truly dreadful AV+ system, which combined single member constituencies using the alternative vote and a minor top up element based on one or two list seats per county or city area. The effect of this system would probably have been to gerrymander the electoral system against the Conservative Party. The Tories would probably have lost more constituency seats than they would have gained (as at the time most Labour and LibDem voters would have preferred either of those parties to the Conservative Party), without the top up element being large enough to produce a fair overall result.

However despite watering down proportional representation, almost to the vanishing point, Jenkins proposals did not lead to a referendum.

The only merit of some change is that might lead to a gradual expansion of fair votes, on the model of the expansion of the franchise in stages during the 19th century.

However, since 1997 and the Jenkins report, we now have much more experience of proportional electoral systems in the UK, so I do not see why we should be saddled with either AV or AV+.