Short (3-7 days) cruises originating in the UK

Your best bet is to go to Vacations to Go, CruisePlum, or another cruise listing and put in your parameters and see what comes up for UK. There are quite a few destinations that depart from the UK. British Isles cruises, Baltic cruises, Norway, etc.

MSC do a weekly circuit from Southampton to Hamburg, Zeebrugge and Le Havre, 7 days for the full circuit.

A round the UK takes between 10 and 14 days as would a Baltic cruise.

This is the full cruise Schedule for Southampton- the biggest cruise port in the UK- the most likely one you'd sail from-

https://southamptonvts.co.uk/Live_Information/Shipping_Movements_and_Cruise_Ship_Schedule/Cruise_Ship_Schedule/

You might find a few on Windstar. Note that there is less profit profile for 3 or 4 day cruise, so you have to expect a smaller ship with lesser amenities. I noticed that eastern East Anglia was very ... boat-y. We easily booked a one-day (crewed) sailboat to go to an offshore children's book site in (I think) the Essex moors.

Fred Olsen have a 5 night cruise from Liverpool to Scotland on 26th August. If you can come a bit earlier that could very easily fit into your Yorkshire plans and flying in and out of Manchester would fit perfectly.

Also on 26 August "Fred" as Fred Olsen are affectionately know have a 5 night one way from Newcastle to Andalsnes and then Bergen in Norway (flying back from Bergen)- that weekend is August Bank Holiday in the UK.
A Norway taster one way is quite unusual.
P and O have a number of 7 nighters ex SOU-
26 August and 15 September Norwegian Fjords (with Marco Pierre White)
27 August Guernsey, Vigo, Porto and Lisbon
2, 7 and 9 September Norwegian Fjords
2 September Cherbourg, Vigo, Porto and Lisbon (with Sue Barker)
19 September Rotterdam and Le Havre (5 nights, with Ben Fogle)

I did check the American lines out of the UK last night but they all seem to be doing longer itineraries at that time of year.

On 2 September Ambassador Cruises also have a 3 night Belfast to Liverpool to Bristol (Portbury).

There are a number of boutique (and expensive) cruise lines (means small ships) which operate short cruises in the Western Isles and Inner Hebrides of Scotland.
Those include the Vic 32- an original clyde puffer- a real steamship which originally delivered goods around the western isles (think the Para Handy tales, if that translates across the pond). She sails 5 day cruises from the Crinan Canal (Argyll) to the Inner Hebrides and around the Clyde, and on the Great Glen (Inverness to Fort William).
But I am assuming that you mean bigger ships- what most people think of as Cruise Ships.

The world's last steam ocean going paddle steamer ship the Waverley makes various journeys around the island of Great Britain.

https://waverleyexcursions.co.uk/welcome-aboard-waverley/

Some short, some longer.

The schedule isn't out yet because she is in annual dry dock but as soon as she is back in the water it will be.

Could be a bit different and very fun.

Waverley has not yet gone to dry dock, that is in several weeks time (see edit below), but it now looks certain that there is enough money available after an appeal for the dry docking to go ahead.
Her Scottish timetable for May and October is to be released next weekend (news released 18 hours ago as I write).
In early September she will be on the South Coast and the Isle of Wight, then on the Thames between September 22 and October 8 (which includes piers in Essex and possibly up into Suffolk).
South Coast sailings include ones along the Jurassic Coast, and to Swanage for the Steam Railway.

If you are in Southampton it is also worth looking for day cruises on the SS Shieldhall- she sails in the Southampton and Isle of Wight areas, and at the start of September to the Bournemouth Air Show- a unique opportunity to sail on a historic vessel and see the Air Show from sea. If you are in the area anyway an opportunity not to be missed. She was built as a Glasgow sludge boat but always designed for day cruising "doon the watter" on the River Clyde.

And if you're ever in the Liverpool area a day cruise on the "Danny"- the steamship Daniel Adamson- is a must. She is an art deco gem with a tremendous history including service in WW1 and conveying a number of members of foreign royalty at various times. She sails mainly on the River Weaver (which includes the engineering marvel of the Anderton boat lift), but a few times a year to or from Liverpool Albert Dock.

And Mersey ferries have their Manchester Ship Canal cruises back for this year- from Liverpool to Manchester- in September on 4, 5, 20 and 21. These are the only usual scheduled ship canal cruises- a 5 to 6 hour passage starting from Pier Head, Liverpool and ending at Salford Quays, Manchester. They also run on various other dates during the year-see the Mersey Ferries website.
So you could combine the Danny with the Ship Canal cruise.

EDIT 16 MARCH 2023- Paddle Steamer Waverley has gone into dry dock today, timetables are being gradually released but there remains a funding shortfall for her dry docking.

Thanks very much for all the info. I think I have enough to plan my trip

did any of our suggestions make the cut or did you find something else?

cruisecritic.com would be a great source of information for cruises.

Funnily enough I've only had an e-mail today from the Lord of the Glens about her cruises from Inverness to Fort William, Oban and the Inner Hebrides-
https://lordoftheglens.co.uk/
Some of which are as short as 5 nights.