Increasing gear ratio on my bike

Hi,
I recently bought boardman road pro carbon slr 2014 second-hand. Unfortunately, the bike comes with quite a limited gear ratio, running 53/39 on the front and 11-25 at the back, and it has an ultegra 6800 short cage rear derailleur (whole groupset is ultegra 6800). I am basically looking for a relatively cost effective way to increase the gear ratio.
In terms of what I want from gears, I live in London and ride regularly but only casually. Obviously the hills are not bad here at all, however on the last few rides I've been on, on steep sections the burn has been pretty considerable on 39/25! Outside of lockdown I would usually do approx fortnightly 100km rides to Kent, which is obviously more hilly but not exactly the Pyrenees. I would just quite like a ratio that would permit me to stay in the seat more and maintain a higher cadence.
So from what I've read, these are my options - although I'm no expert at this, so please correct me if I'm wrong anywhere:
1) Buy an 11-30 cassette - the short cage derailleur I believe can only handle up to 30 teeth (I think Shimano technically says 28, but apparently 30 should be doable) - price approx £35
2) Buy an 11-32 cassette and medium cage derailleur - I think from what I've read the shimano medium cages can handle a 53/39 and 11-32 at the back, although I'm not 100% on this. Price approx £70. This is with buying the 105 R7000 medium cage rear derailleur. I would love to maintain all ultegra, but feel it is a little expensive, however any advice on the differences between them, and any limitations of mixing would be appreciated.
3) Buy a compact crankset and a cassette and possibly a medium cage derailleur - I can get the 105 R7000 compact crankset for around £90 and then would be obvs be the cassette/derailleur cost on top of this. Again any advice on ultergra/105 differences/compatibility.

I know there's not really a question in there, but any advice you guys could offer would be very much appreciated!

Cheers

I'd go for option 1) and see how you get on... 30t is a big difference to 25t - it'll feel like having 2 or 3 extra gears below your current 25t lowest.

Don't forget to change your chain too if you've done any significant mileage on it (i.e. more than 1500-2000km).

Also, just checking, are you using clip-in pedals and shoes?

Agreed, option 1 is the cheapest and easiest. Go for compact chainrings long term, keep an eye out for second hand stuff

Hi,
Thanks a lot for your replies. That had been my inclination also, so it's good to hear it from someone else - and then reassess when I've seen what difference an 11-30 makes.
Yep I am clipped in, so that's at least made the grinding up hill a bit more tolerable!
Cheers

Your going to wear chainrings, and they cost a lot! Change those when worn.

I’d just whack a 30t cassette on there and hope that’s enough.

You could use an extender for about £5 and then go up to 34t I reckon.

Also, change your use of the word ratio for range. Range is the spread of gears, ratio refers to the specific sizes.

Only potential problem is that when you go big chainring and big sprocket you’re setup may not have the capacity to allow the chain to be long enough.

Compact crank is your safest option.

The short cage can happily handle 11-32. Shimano are very conservative on their specs.

Assuming the chainset is Shimano 6800 you don't need to replace the crank arms to switch between 53/39 and 50/34, just the rings.

There are no compatibility issues mixing 5800/6800/R7000/R8000 parts that I'm aware of*. They're mostly functionally identical but 105 level components are made using slightly cheaper processes that make them very slightly heavier.

(* Though I wouldn't use chainrings that don't match the crank arms)

I would disagree that a short cage can ‘happily’ handle a 32. Some frames that have a long hanger might handle it but it doesn’t happen very often.

Buy a triple. All the cool people are riding triple now.

I mean, we now have three triples in the shed...

outweighs everything else.. 2 doubles, 1 balance bike, 2 singles.

When you say ‘outweighs’, you mean figuratively, or actually weighing more than everything ;)

I have two bikes with triplez. Both Thorns 👍🏼

I think both!

Our thorn has 5 chainrings! (Not including cassette)

Oh really? Think perhaps my knowledge on cracksets is a bit dated and generally deficient. I've always thought that standard vs compact involved different BCDs.
Ah yes, have just looked it up and ultegra uses 110 for all? OK, that is definitely good to know for pos switching to a compact down the line.

I got 53/39 front and a 30 cassette in the training wheels and works great with a short cage.