Not sure about Brid, but dogs are allowed on Filey beach, at either end. Both sides have a slipway onto the beach, so easy access for a pram. If you head to the right hand side at low tide, you can walk for miles, it's stunning. Dogs are allowed on the whole beach out of season (I thinks it's from the end of Sept). The same goes for Scarborough.
The beach at the far end of the esplanade as you walk out of town is dog friendly all year...The nearer the town you get there are seasonal restrictions with timetables posted as to when you can take them on...As I found to my cost when I wandered into one of these zones along the shore line from the dog friendly part..One or two people(to whom I am grateful)Pointed this out to me before the warden got me...Beach at North Landing has no restrictions and can be reached with a pram via a steep walkway...Ok going down...Bit of a grind pushing a pram up..As I well know having done it several times when my kids were young...
Jelboy.
------------- Campers of the storm,Into this world are born
For Brid, If you park up at Wilsthorpe, where the Park and Ride car Park is, behind South Shore Holiday Park, the beach there is dog friendly. There are loos on the car park too, which is always a bonus if you're planning on staying for a few hours.