I think you are going to have to remove the whole lot, weeds, grass and gravel and start from scratch. There may well be an old, partly rotted barrier membrane under the gravel which the weeds and grass are growing through.

God luck Agent O and welcome to GoY

ok, so you rent -that mean you no want to pay -much anyway - MG is corect but i thinkin slow mesy way -use a spade an dig out smal space here an theer lik a pachwourk -this wil help you pick out hte gravel from wheer hte grass stil ius - an to shake out hte gravle from hte turves you hav lift. hten rake wole area htrow back hte grass you hav lift and tred in. wiht time, hte grass wil all grow bak an you no spend a penny,well, apart from constent trip to tiolet fro all hte tea you wil be drinkin, cos hte hard work!

Mexborough eh, that brings back memories. One set of Grandparents lived there when I was a child and I visited regularly.
I agree with the two previous responses and I am afraid that you are in for a lot of short term hard work! The gravel and grass has to be dug out and removed before you can start to get a decent surface to sow a lawn in the spring.
If you have the time and the energy then it can be done and you will end up with a nice lawn. You possibly need to consider how long you expect to be living in this rented house. If you expect to rent for a good number of years then the work will be worthwhile but, if only for a couple of years before you move on then it might not be worth the effort.

i also suggest you check with the owner that they dont mind you doing this.
and if they say ok then you have chosen a good identity agent orange. :o)
welcome to GoY too.

I like all the advice put forward so far, but the advice put forward by Dereke is very well thought out, but if you can aford it or have an obliging frend get a rotovater over it and rake out the grass , the pea gravel will sink and become good drainage , then if you have no roller get a plank or two and walk it flat by puting the planks or boards down and walking on them all over were the lawrn will be, then either turf or sow seeds, but dont bother yet let's get rid of this foual weather first,

cliffo - very well thought out,to - high fives! (smak) :)

Thank-you, will use a combination of both ideas, (Dig it all up, give decent sods a shake & use to patch up some grassless bits in back garden & re-seed front garden)

Sbg; I made a point of asking the letting agent about that ;-) They said; 'As long as it's improving the property you can do whatever you want.' :-) If you saw the state of this front garden I think you'd agree, that it's almost impossable to make it any worse than it presently is. lol :-)

sensible precautions; enjoy your self then

Good luck AO - have fun!