It is a common misunderstanding that getting people to work harder for less is the way to get to higher productivity. It isn't. And in lots of parts of the economy it simply can't be done. The classical example is a string quartet playing a Mozart work written more than 200 years ago that takes half an hour to play. More than 200 years later it still needs 4 people and half an hour to deliver the same output; nothing can be done to improve their productivity, the 4 people can't play faster, nor can they perform with only 3 people.
A better way is for people to move from a low productivity job to a high productivity job. In ye olden dayes of large bureaucracies, this was done mainly by getting promoted. Now it has to be done mainly through job mobility, and the UK economy doesn't have enough of it. That's partly down to lack of workers rights on day one, losing those rights when people start a new job is a significant disincentive to job mobility. But a far more significant impediment to job mobility is the UK's highly dysfunctional housing market, which has huge incentives encouraging people to stay where they are, and huge disincentives discouraging people from moving.
When automation came to manufacturing, few people could foresee that the jobs would be replaced by call centres. Technological advance will create new jobs, as it always has done.
The best way to improve productivity is to get out of low productivity industries/services and into high productivity industries/services. The UK actually has some excellent opportunities to do this in fields such as life sciences, artificial intelligence, clean energy and entertainment.
The UK needs to concentrate on developing these, not continuing with its obsession with creating/retaining more low productivity jobs, notably in what these days is called hospitality. The UK economy isn't going to get more productive by having more people selling each other cakes and ale. This is particularly perverse in a labour market that has reduced supply because of demographic changes. These can be partially addressed by higher workforce participation, but equipping people with the necessary skills is more important.