Heathrow Express Voucher 2010 Are Dogs Allowed On The London Underground Or Heathrow Express?

Are dogs allowed on the London underground or Heathrow Express? - heathrow express voucher 2010

I'll help a friend to move his 2 dogs from Heathrow to Glasgow by train to Heathrow to fly with them () without quarantine, so I think we have to arrive at Paddington Station, and seem to take the train to Glasgow, that dogs in the moves are allowed, but what happened to the airport to the station, dogs allowed in the subway or the Heathrow Express?

Thanks