Hi all, is this something I can reasonably adjust myself or should I get the mechanics to sort it when I get my tyres sorted. Thanks!

how long have you owned car. how long has it veered right. 

Did it start doing this after an event eg. hitting a kerb / large pot hole.

If you can not see anything wrong eg. bent suspension etc the first thing I would probably try is swapping the front wheels with eachother and seeing if that makes any difference.

Of course if your tyres have directional arrows on (some do some don't) you can't really leave them the wrong way round, but it would not stop me testing it that way.

This could be quite hard to track down the cause without wheel alignment equipment if nothing visibly bent and swapping wheels makes no difference

I think it's been happening since I've owned the car. I used to have an MG that veered left slightly. So I noticed right away the Fiesta veers right.  

 

I think it's also been getting slightly worse over time. I do live in an area with atrocious roads which isn't helping. Thanks.

Most tyre places do wheel alignment as well and it doesn't cost a lot of money. That will almost certainly fix the issue.

If you take it to a decent enough place for a wheel alignment then they will check to see if anything is obviously bent after being hit into. The horrific condition of UK roads means it's very easy for the steering to come out of alignment.

It's not unusual to have cars veer ever so slightly to the left due to the slight slope on the roads.

Kind of stealing the thread, but as Luke4efc said, it is not uncommon cars to veer. Is it possible to change the aligment to minimize this(putting more toe or is it less? ) without wearing the tyres quicker?

pulling to the right is normaly due to worn / iregular tyre wear. swapping wheels front to back usually confirms this. 

whether it has too much toe in / out    or    too little toe in / out   should not make it veer one way.  Yes it does affect the self centering effect but if adjusted poorly it will self centre too much or too little, but should not make it always go right.  (as mentioned above, going to the left can be a commonly perceived problem, but down to camber of road).