As long as the timing doesn't get too much further onto the other side of a couple of hours, it can work out just right anyway, considering that once you deboard your plane, you then have to get yourself to the luggage area (which for me at Gatwick seemed like an endless walkway-walk across the entire airport!), wait for your luggage, grab your luggage, another long walk to find and get to the immigration/border desk area (don't suppose that's the official name but it's all just a blur to me now) wait in line there, get checked through there......
By the time I had cleared all these and finally got to call the ARC to see how my cat was faring, they told me they had (by then) already dealt with him, said he was great, and the time they told me to come and get him was almost upon me; we had a beverage then we made the drive over there. As far as I remember of my own experience, it seemed to work out over two hours anyway.