The first thing to do is decrypt and rip the movie to the hard drive. If you can use MKV format this is easy to do with MakeMKV, a free decryption program.
You can also do a complete copy using DVDFab if you prefer. Don't change format, and don't let it compress anything, just a full copy.
When using MakeMKV with DVD's the output is always a main movie only MKV file that isn't compressed in any manner. To add the .srt file, you use MKVToolnix, another free tool. In the MKVToolnix GUI, you right click inside the top box, which gives you the option to add files. Bring in your MKV file from MakeMKV and the .srt file. You'll see that it automatically makes a destination for the combined files, but you can change this if you want. Then click on the Start Multiplexing button at the bottom. That's it. Very simple.
If you rip with DVDFAb, the Vob files can be combined with Vob2Mpeg, then imported into MKVToolnix, but I find it easier to just use MakeMKV for ripping to an MKV.
Now, if you want a DVD-video, things get more complicated. Rip to the hard drive and make a single file from the movie, either with DVDFab/Vob2Mpeg, or MakeMKV. Now we use another free tool called AVStoDVD.
Open AVStoDVD and click on the green + sign to import the video. If the .srt file is in the same folder and named the same, AVStoDVD will probably find it and ask if you want to import it as well. If not, the video will show up in the main screen of AVStoDVD as a new title, so right click on it and you will see a list of options, one of which is subtitles, where you can import the .srt file.
AVStoDVD will compress to fit a single layer DVD unless you change the output setting. Also, since your movie is from England, it is probably in PAL format. If possible, you want to let AVStoDVD keep it in this format, but if your player cannot handle PAL DVD's it is possible to convert to NTSC using AVStoDVD, it just won't be quite as smooth when it plays.
Other things to note. You'll need to install the package for AVStoDVD, which includes Avisynth. Its all taken care of with the installer, but thought you should know. I prefer to use AVStoDVD with the HC encoder set to a 2 pass encode. You'll see that option when you install.
Both of the methods I've outlined loses the original menu and extras. You can make a simple menu in AVStoDVD if you wish, but not necessary. It is possible to take the original DVD and add a subtitle to it, but this gets very complicated using free tools like PGCEdit. DVDRemake can probably do it as well, but it is a commercial product.