Decathlon is opening its store in Northarbour tomorrow (Thursday 25-April-2018), near the Tesco Extra, and they're offering free backpacks for the first day if you have a Decathlon account and card.
They do a fantastic range across all sports at great value, but especially cycling, and their bikes get great reviews. Disclaimer: I bought one of their fantastic folding bikes, and it's the most fun bike I've got - I'm certainly recommending it.
Previously, the nearest store was West Quay Southampton, which is a bit of a trek for us here.
More details at https://www.decathlon.co.uk/portsmouth.html