Answer:
It very much depends on the cause and extent of the tachycardia Any arrhythmia is considered important and deserving investigation before clearing an individual for diving because immersion has its own influence on cardiac patterns.
Causes of tachycardia such as Wolf-Parkinson-White and Lown-Ganong-Levine have been known to be associated with congenital cardiac defects and require specialist referral. Betablockers are contraindicated in diving as they may affect the original dysrhythmia by increasing its incidence, its frequency or its haemodynamic consequences or induce new dysrhythmias due to their effect on re-entrant circuits or due to marked QT prolongation.
They may produce more bradycardia, aggravating the immersion reflex any also increase ectopic beats. As for the UK rules, these are only binding on those divers who require an annual HSE medical, that is professional divers, and such a condition would probably be failing. Recreational divers in the UK are only required to fill in a health questionnaire (and this is not a government but a diving industry requirement) but common sense should apply.