I babysit for some twins (have known them since they were very small, now they are 21 months old) in Windlesham. Will send their mum an e-mail and see if she can suggest any groups which are twin specific.
Meanwhile, Woking Twins Club holds a Parent & Toddler group in Knaphill on Monday's 9.30-11.30 St Hugh of Lincoln Church (Parish Room), Victoria Road, Knaphill GU21 2AA More details...
If you want more general toddler groups then: Drop in group run by NCT. Every Monday 10-11.30am (closed on Bank Holidays) Holy Trinity Church, Church Rd, Sunningdale, SL5 0NJ
St Michael's Parent and Toddler Group Wednesday 10am- 11.30am St. Michael's Church Hall, Church Lane, ASCOT, SL5 7DD
Sunningdale Parent and Toddler Group Tuesday from 10 - 11.30am Baptist Church Hall, High Street, Sunningdale, SL5 0NG
There is also a Coffee & Chat group that meets at Sunningdale Venues / CMI Rendezvous Cafe at 10.30am on Fridays.
I went to a toddler group in Bagshot on a Wednesday 9.30am-11am at St Annes Hall, Church Road, Bagshot, Surrey, GU19 5EQ for many years when I used to nanny on a Wednesday (currently I nanny Mon,Tue,Thur,Fri).
I found that I had to experiment a bit with baby/toddler groups to find ones which fitted with me and the children in my care. So once groups restart in September, visit a selection in the area and see which you and your twins like.
The mum of the twins I babysat has got back to me. Alas she does not go to any twins club and neither do any of her friends with twins.
There are other toddler groups around, such as in Lightwater, Windlesham, Chobham.
Is it you who would be taking the twins, or your wife? I'm always up for meeting local people - baby I nanny is now 9 months old. Are you able to travel, or are you specifically looking for things in Sunninghill/South Ascot?