Before you decide on not doing pullups I would look around your home and outside and see if there is something you can do a pullup on. When I'm at my mother in-law's place I find the nearest acceptable tree branch. Sometimes you can find something in your house that you can use such as a ledge or a fixture. worst case scenario you could do door pullups. Not quite the same thing but about the closest you will find if nothing else is available.
If you don't have a bar I would look at ordering one. You can look on the main website here and order one if there isn't a sporting goods store in the UK that carries one.
For this program to work efficiently you really need to have access to pullups. There are substitutes such as using weight machines but it still isn't the same thing and really just isnt a good substitute. Free weights doing rows can sort of substitute but again isn't the same thing. I worked out with a guy many years ago that could do dumbell rows with 120 lbs but couldn't do more than a couple pullups.
Your case is not unique and many people find this a stumbling block but you just need to get inventive and find a place to do pullups. I guarantee you there is one there somewhere. heh.
"Permanence, perseverance and persistence in spite of all obstacles, discouragement, and impossibilities: It is this, that in all things distinguishes the strong soul from the weak”