Afraid I don't share your keenness to avoid lethal measures - releasing them just guarantees their return I think. 

Patience is annoyingly a pretty fundamental requirement when it comes to trapping vermin as they're very apprehensive of new things. I've always found a cheap PB does the trick when we've had mice etc. 

Humane ones are absurd. Where are you going to put the snarling rat?

Yep, patience I’m afraid. 

We had a mice infestation last year and used those traps you’re using. We also found sticky mats effective and caught three that way. Our mice were little though, your rat sounds big.

Humane ones are absurd. Where are you going to put the snarling rat?

We released our mice into nearby woodland.

Rats are definitely a different proposition to mice. We had recurring problems with them when we kept chickens. I got quite accurate with the sharp end of a garden spade but you may be a little more squeamish...

Rat poison works a treat. Just put it in a bowl so you can monitor it.  PUt it out every night and eventually it will go and so will the rats. 

There will be more than one rat

Rats are attracted to food - so take away any bird feeders or simlilar. 

or find someone on facebook with a gun. Lots of hobbyists will lie in wait and shoot them at dusk for you.  

There are more per sq ft in city offices

Some even have their own desks

slaymore

my cats will take down rats. They have done three this year - two of them pretty big.  The neighbours have chickens and we are quite rural. 

Where we used to live we had loads as we had lots of animals and we were able to control them through poison - but you have to take it seriously 

They like undergrowth so keep all areas mowed short. Keep all food away in metal tins / bins.  If you are using poison put it up against the side of a building, as they will rarely break cover.  You shoudl be able to see tracks of where they go.  

BB Gun. PLINK

One person poke where it is hiding with a pole, second person hits emerging rat with a shovel. Hang it up for its friends to note.

if you're seeing the rat return to the same place.. you have many rats.

Either get a cat or a Jack Russell, that'll deter them.

Mice and rats have homing instincts so will return if you "release" them

spiders do this too.  If you throw them out the window, they come back.  You have to get them at least 12 feet from your home.

Similar issue last year - pest control chap set a few 'Black Cat Rat Traps' which apparently are the dogs bollocks of the pest control world.  Personally, my approach would have been putting down some stinking cat food and laying in wait with an air rifle but Mrs Fishfingers was less keen.

Are you sure a garden office has a cavity wall? That would be ludicrous expenditure. Most are constructed on a deck and like decking rats love living under those. If you have that, you get steel mesh that you staple to the "skirt" of teh deck and then burry about 1 ft into the ground beneath. 

funnily enough I’ve just watched a rat chase a blackbird off one of our raised beds - think he’s moved in under the compost heap. ive sold my FAC .22 air rifle (incidentally I was amazed to discover that in good ‘ol USofA you can get .50 cal air rifles!!! pre charged of course) anyhoo I’ll be getting some “Big Nippers” - presumably you can still get those? - and with a bit of proper fieldcraft I will terminate the varmints with extreme prejudice. 
Unless you are absolutely sure they’re not getting into any buildings DO NOT USE poison because they’ll die under the floorboards or wherever and create an unholy stink for months - really terrible smell. Plus if they’re full of poison outside an owl might eat it and then you’ve got a dead owl. Cat eating poisoned rat is good but some might disagree. 

our problem is silly neighbour woman who puts out tons of food “for the birds” but doesn’t understand that it needs to be done in a disciplined way so only accessible to songbirds - throws bread on the roof of her shed, feeders in the bushes (rat and squirrel heaven) and overflowing feeders - enough food for every bird in the south of England- oh surprise! We’ve got rats!

Are you using smooth or crunchy peanut butter?

the rat I saw today was average build - the one I saw a few days ago was an absolute porker: I think he’d added bird food to his elvis style smooth peanut butter and jelly sandwiches. I’ll be fat shaming him next time I see him (or her) - the gluttonous rat pig. 

We once had an enormous rat when I was a student. We nicknamed him 'champ junior's.

He was completely non phased by human beings (he would saunter slowly beneath your chair and between your legs in the kitchen for example) and he seemed totally invincible to all kinds of poison and traps.

Eventually what we did was we got some kind of special spray from Hong Kong (housemate from Hong Kong) and we just blasted the entire can into his little ratty face while covering our mouths with cloth so we didn't kill ourselves as well. That didn't seem to kill him but we eventually found him curled up in the garden outside dead. He looked like a furry rugby ball.

I think the incubation period for humans is 20/25 years for that stuff Buckaroo. 

I don't care prodigal. Champ Junior was my white whale. It was either him or me.

And if it has to be both of us.

So be it.

Perish the thought of you also ending up looking like a furry rugby ball. 

Update:

Thank you for your comments and advice. The rodent continues to evade capture. 

We do have a Jack Russell but he is useless (evidently).

Reluctantly, I have loaded my air rifle (a .22 HW95K, non-FAC) and set up a firing position from my son’s bedroom window.

Problem solved.

FFS. Parsnip is correct. After disposing of Roland’s lifeless furframe, Rachel has now appeared.