I need a climber that will happily live in a pot . Sheltered but sunny area

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We have a block paved area in our garden that has walls/fence 3.5 ways round .
Once side isn't ours so cannot put anything on it . Other side is part our wall.
Theres a fence but I don't want anything attached (like a pergola type) as its access .
We're putting trellis and wire support for them to climb on.

So.....

I want a rambling climber to give the illusion of the Med (we're in East London so quite sunny)

I have a Clematis planted in soil , its doing well
I have 2 passionflower in pots so far (huge pots)
And nastursiums and sweetpeas

Don't like honeysuckle .

Something like a grapevine but less fussy ?

TIA

Climbing hydrangea
Some roses do fine in pots, Gertrude Jekyll for example and you can train up a fence

climbing annuals are good fun - thunbergia, Spanish flag, rhodochiton. Check out Sarah Raven for pictures and see if local garden centres have any but I've grown them from seed with great success.

Thanks ,
I hadn't thought about roses . I used to have a Paul Scarlett climbing rose , it covered one wall of the garage (but not in a pot ) it's long gone now sadly .

When I went to our local Homevase there were a few clematis and a load of wisteria .

I have just planted Morning Glory in two big pots (glad it is contained, it has gone crazy and is rambling everywhere) Grows extremely quickly and is pretty.

Jasmine?
Hops?
Abutilon?

Hops have grapey leaves?

Bougainvillea?

There's an ID thread on here about a plant called Stauntonia. Could be worth a look?

Friday’s Gardeners World did a feature on Clematis. The contribute had lots growing in pots

A summer jasmine-smells divine all summer every time I go in and out of the house

I've ordered a Hop for the bottom of the garden . I like the look of them and they look a bit unusual .

I need a climbing rose too , we have a metal arch that DH is waiting to assemble so that's my next search