There are plenty of good train options to various parts of the Cotswolds. If you're staying south of the venue, near Cirencester or South Cerney we recommend:
London Paddington → Kemble (1h 8mins)
Birmingham New Street → Kemble (1h 33mins)
Oxford → Kemble (1h 6mins)
If you're staying north of the venue, near Burford, Bourton or Stow we recommend:
London Paddington → Kingham (1h 18mins)
Birmingham New Street → Kingham (1h 30mins)
Oxford → Kingham (25mins)
Taxis in the Cotswolds can be a challenge. To avoid any surprises, we suggest booking one at least 24-48 hours in advance. You're a long way from Uber.