Airports

Jerez airport
Jerez's airport is 15 minutes from the city centre.
From London, there is a direct flight from Stansted (Ryanair) every two days (i.e. Thursday 6.30am and now Fridays at 14.30pm) and return on Sundays (10.40 am).
There are daily flights from Madrid.
Seville airport
A good alternative, with more flight options, is Seville airport that has flights from many European cities (Lisbon,London,Paris,Brussels...).
There are daily frequent trains from Seville to Jerez (1 hour) and driving is 1h30 to Jerez.
Train tickets can be purchased here: https://www.renfe.com/es/en
Destination: Jerez de la Frontera

Trains
There are daily and frequent trains to Jerez from Madrid
For tickets, visit this website: https://www.renfe.com/es/en