I think that anything that could be construed (or misconstrued) as pressure is wring.
The key thing here is that he has agreed in the past.
Did he actually mean it, or was he saying 'yes, yes' to make the issue go away. If he did really mean it, then make an appointment for him (go with him if necessary).
Remember that, despite being carried out under local, it is still surgery and has a 10% risk of the serious side effects (source: NHS, others pt it higher; serious means painful, enduring and need significant intervention to treat (further surgery) or are untreatable even by de-nervation). If it turns out that actually he does not want a procedure with those risks, then it is his body and his choice.
If he does go ahead, check likely waiting times, be aware that it usually takes 8-16 weeks to test clear and can take longer. You'll also need to decide on contraception for what could easily be another year
If NHS lists really are dire in your area, then consider private eg at a Marie Stopes. It's not that expensive, and the doctors are performing vasectomies a couple of days every week, making them considerable more skilled than a GP who offers it, thus reducing (though not eliminating) risk of operator error