In addition to the services listed below there are also frequent coaches from many towns & cities (and Heathrow Airport) to Bristol, where you can connect with the 376 local bus to Glastonbury.
Connecting Glastonbury, Street & Shepton Mallet to London with a single service. Coaches depart London at 17.45 and Glastonbury at 08.30 (Sundays & Bank holidays have different timetable).
Timetables & Fares on the website . Select Superfast 3 from the options.
Low cost inter-city travel with several services to Bristol from where you can get the 376 local bus to Glastonbury.
There is one daily National Express coach service (403) that directly connects London and Glastonbury. That departs London at 18.00 and Glastonbuy at 06.50 - hence it is not possible to do a day trip from London by coach. However you can travel to Bristol and then get a local 376 bus to Glastonbury.