The 2311 does call at Reading
Swindon (Wilts) 23:11
Didcot Parkway 23:28 23:30
Reading 23:51
Train continues to London Paddington
The East Coast website actually suggests changing there
Reading 00:04
Twyford 00:10 00:10
Maidenhead 00:18
Train continues to London Paddington
However, if you have an advance ticket, you must travel on the trains shown on the reservation.