Only you know if it can work...what anyone else says really doesn't matter...and please don't take advise from people who know nothing about Islam and your partners culture...and there IS A BIG DIFFERENCE. For the record I know nothing about Bangladeshi culture (so only half listen hehehe)
I am a British convert to Islam, and converted about 8 years before I met my DH.
My DH is Muslim of North African origin born in the UK.
We have been married 5 years and have a beautiful dc and 1 on the way.
Islamically your relationship can work...as previous posters have said there is no religious reason why you have to convert, Muslim men are permitted to marry a Christian. Be prepared though, as any kids would be expected to be raised Musilm...are you happy to see this happen?
With regards to conversion, I would never be able to support a woman converting purely for the sake of a man, it's hypocritical...you'd be living a lie, and how can anybody ask you to do that, and most of all there is no religious need for it, don't let anyone tell you otherwise!!!
I do strongly recommend that you try and understand as much of the basics of Islam as you can...it will help you to understand alot of the things you may encounter and you need to know what any future kids may be taught...I also think it's hugely beneficial to be able to differentiate between culture and religion yourself, you can save alot of pitfalls that way, and hopefully make your life a little easier, and most importantly know what any future kids are being taught.
Culturally m'dear I'm affraid its a whole other ball game, there are so many factors that I can't honestly comment on, like I said. i've had little to do with bangladeshi culture, but from my own experience...
Stay strong, you are British (i'm presuming!, forgive me if i'm wrong) you don't have to compromise that.
Don't do ANYTHING you are uncomfortable with.
When it comes to his family, compromise is nice...the little things that are inconsequential in the big scheme of things may mean alot to them...eg wearing traditional dress when visiting, integrating into community when visiting, having a go at the language...if only for their entertainment lol!
I had a rule for myself about family when it came to getting married...if they have a problem and don't support the relationship, don't waste your time...saying that, I know people who've had problems with in-laws from the start but made it work, and others who have had the most welcoming in-laws at the start who became monsters afterwards! I think the same can be said of unicultural relationships too though
As other posters have mentioned...PLEASE BE AWARE OF THE VISA THING...what's your other half's current residency status...be cautious, there are horror stories...if its questionable, considerations may include having purely an Islamic marriage, not recognised in this country and therefore will have no impact on your OH's citizenship. Whilst i'm sharing my rule for self regarding this was no UK passport no marriage...but you know what I am a bit of a cynic!
At the end of the day, the culture thing all comes down to giving it a go, time and experience...alot of it will be so personal to your individual circs, I can't say it will be easy, but then which relationship is? I know lots of multicultural families that work brilliantly, and the kids are offered such a great outlook on life, ultimately getting to choose the nice bits from each culture, and understanding more of the world than the rest of us ever could.
Good luck!