We booked a room at the Premier Inn West Quay for the Sunday night prior to a cruise next August. Looking for a suggestion of a pub within half mile walking distance of the hotel. Based on past experiences of being a Walk-In on a Sunday (roast day) elsewhere in England, we'd probably need a reservation, correct? Plus it's a bank holiday weekend! Thanks!
There are a number of pubs in that area but not all have Sunday roasts. When I don't know an area (and just in case you don't get a personal rec), I use Google, which showed a number of pubs within a mile. There are two that serve Sunday roasts and are approximately a 7 minute walk from your hotel, so within your parameter.
The Duke of Wellington serves a Sunday roast from 10-4 and has very good reviews on Google.
https://www.dukesouthampton.co.uk/bookonline
Also, the Red Lion Pub serves a Sunday roast as well, has good reviews and is approximately the same distance from your hotel. https://www.theredlionpubsouthampton.co.uk/
You can book ahead at both of these places.