I encourage you to speak with your GP and associated midwife for family planning purposes. It is particularly important because each practice will have a different methodology here--just like in the US. So, you need to find out if your practice is the right one for you. You have the time now to figure out if you need to switch.
The NHS will not offer you upfront testing beyond standard tests that start around 8 weeks of pregnancy. However, like the US there are private practices that you can visit if you desire advance screening. One of the most reputable is the CARE clinic:
http://www.carefertility.com/ It is expensive to have some of these tests, but it does not seem to be much more than US clinics.
Generally, the more complicated testing or IVF are only available through the NHS if you have had three miscarriages. It is important to note that if anyone has a miscarriage--even after only a few weeks--it is imperative to go to the emergency room to have it reported. One needs the documentation to merit the the later treatments. Also, it is worth going because post-miscarriage care in the UK can (not always) be impressive. In this area of the midlands, at least, there is a department of specialists and after one miscarriage, it is possible to arrange for screening in earlier weeks of pregnancy--around week 7 to see if there is a heartbeat.
After three miscarriages a woman is then eligible for one round of IVF as suported by the NHS. Even then there are standards. There are age requirements and weight requirements.
Best,
Rutabega