Pilch,
The CAA can supply the kit. They are in short supply and you may have to wait. You have to wear the thing for 24 hours, during which time it takes your systolic and diastolic pressure readings together with your pulse every 30 minutes.
"white coat syndrome" is very common and I am surprised that a borderline reading caused them very much concern. B.P readings do vary throughout the day and it is usual to take a number of readings over a period of time. Worry obviously doesn't help you obtain a better reading.
You can buy your own monitor for around £100 and it is a sensible investment if you are prone to hypertension (high B.P). You can then take readings at your convenience and plot them.
Hypertension is often symptomless, but has serious potential for illness over a period of time, so it is wise to get it treated if necessary. Often it can be controlled by lifestyle changes ( exercise and diet). It can also be treated with various forms of medication.
I hope this helps, but if you want any further information from my own experience with this problem feel free to e-mail me.