Our new 6 month border collie is now doing really well with his housetraining. We take him out at 11pm and he settles well into his crate. However, every morning he is waking us at about 5am, barking. He is in his crate in the kitchen with our other dog, sleeping outside the crate, who would sleep right through till quite late if left. This has been going on for over a fortnight since we got him. We get up and take them both outside where they always do a pee, as you would expect. We put the pup back in his crate and he will generally settle again until about 6am when he starts barking again.
We weren't too concerned initially as we knew he would take time to settle and also we were anxious to reinforce his housetraining which wasn't fantastic when we got him. He has always been dry in his crate. We did think though that he would gradually extend the time till he woke but this just isn't happening! He doesn't seem desperate to rush for a pee when we let him out and we suspect that his waking time has now become a habit. We are shattered!
Should we just carry on and hope that eventually he'll sleep later or would it now be a good idea to ignore the barking - he is after all learning that barking brings results. I should add that we don't speak to him or give any attention or fuss when we let him out; it's minimum contact.
I worry though that the barking would be awful for our lovely older dog who is right next to the crate and also that all the good work re housetraining will be undone if Hamish then pees in his crate.
I know that there is probably not a 'correct' answer but I would really appreciate advice, particularly if anyone has gone through the same thing.

All sounds completely normal to me, some dogs just take a bit longer than others to go through the night.  Also, if he's still very new to you then presumably he must still be on someone else's timeclock.

I've always had a pup in the bedroom with us for the first few weeks so that I can teach him to settle, offer reassurance and just as importantly learn his timings.  Sometimes when they wake you can just shush them back to sleep but other times it's clear they really really need a pee.  Having them right there does as least mean you get to learn the difference!  I appreciate it's not this simple with an older dog (you can't just carry them downstairs for instance) but it might be worth a try.

Something else I did with my 5 month old pup who just couldn't seem to get past 6am was to take him into the living room with me for a kip after his morning wee.  I lay on the sofa and he'd just tuck in behind my knees and in this way he learnt to settle for much longer.

I don't advocate leaving them to bark - he's trying to tell you something after all (even if you cannot understand exactly what he wants).  But you could try getting to him before he wakes.  Set your alarm for 4.30am take him out for a pee then quietly put him back to bed - you might find he lasts longer this way BUT I'd reconcile yourself to a 6am start for a little while longer.

Finally (yes finish woman, please!) make sure he pees at least twice last thing at night.  If he goes to bed at 11pm go out at 10pm AND 11pm and give him time to pee at least twice each time.  Boys are terrible for going properly and are usually faaaaaar too busy to do the job properly.  Give him time, he'll get there.  My youngest is now 14 months and can easily sleep past 9.30am in the morning - probably longer but I haven't needed to try :)

Have you put your central heating on and could it be the noise of that coming on in the morning that wakes him up?

Heating doesn't come on till 6.30 - how things used to be!
We're trying getting up at 5 or just after before he starts to bark, putting him back to bed (he goes without any fuss) then going back to bed ourselves until 6.30 (still no barking). This is working so far; we'll try making it a little later each week.