Ignoring all of the young and niave on here who have grown up watching movies telling them that love conquers all.. and nothing should stand in the way if you love the person...
Getting into the real world, class is a combination of two things in the UK:
Culture + Wealth
Funnily enough, both of these things are highly important to assessing who to marry. Not who to date - you can date and have fun with anyone, but when you are looking at who to marry, who will become a part of your family, and be with you for the rest of your life, then they become highly important.
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Wealth is the easier one - if you have a person with a lot of it, and a person without much - then its a simple set of questions: Can the person with money help the person without? Share their wealth so they both live on an even level, and can experience everything together? Or does the person with less money have the potential and capability of earning more, and matching their partner? A relationship can never work if two people are at different financial levels, and do not help each other to become a single financial unit.
So say, your family are very rich, and he isn't - and you want to do XYZ rich activities every year.. fly to X for holiday.. eat in Z posh resteraunt.. follow Y rich hobby. If he can't afford it, are you willing to pay for him to do it with you? Combine your money so what's your is his, and whats his is yours etc? Or are you confident that he can rise to the level of income/wealth needed to match your family?
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Culture is the harder one. Class differences in the UK are cultural differences. There is more cultural difference between an upper class British person, and a working class British person - then a working class British person and a french working class person.
I come from a middle-class family, probably on the upper-side, and throughout my life I have had a fair bit of exposure to upper-class families.. and you quickly realize how different their culture is. Its different traditions, different family values, different ways of functioning in the world, different hobbies/interests, different institutions etc. The middle class and the working class are quite similar, but the true upper class, is a world apart culturally.
Culture makes a huge difference when you are considering finding someone to marry.Trust me, as someone who is in a relationship with another person from a different culture (caused by ethnicity not class) you don't realise how much it will effect your life until your into the marriage, and dealing with the issues. It causes so so many more problems for a marriage, when you have two people with different cultures. You have endless potential clashes where one culture would do X, and the other believes Y is the best way.. and it really pushes and forces you to be very good at negotiating/compromising and more.
Your parents are also the big difficulty when culture is considered. Again, from personal experience, I live in the middle of two sets of parents, mine and my wifes, from different cultures and its a nightmare. I can understand my wifes' families culture... my wife can understand my culture... but my parents? They can never understand her culture, and her parents? They can never understand my culture. You are constantly stuck in the middle, as each set of parents has vastly different values and ideals for your life, and you constantly have to mediate between them. Add babies/grandchildren into the mix, and gets even more messy.
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So really its just something you need to think very clearly about. Ignore the kids who want you to forget every practical consideration for love. In fact when choosing who to marry, practical considerations like wealth and culture are very important. That doesn't mean its impossible to make it work - its still very possible, but it means that its only possible if you both understand and are willing to accept the extra difficulties. Marriage is already difficult, its a big thing to make it even harder, so you really need to be ready to make that sacrifice. There is nothing bad or shameful about admitting that - actually you'd like the easier option of marrying someone whose life and path is more similar to you. Its what most people do.