welcome to GoY.
As it is on her property you can not cut it down as you would be causing damage. However you could pop and ask her if she'd mind taking it down so you can have the replacement glass done.
Perhaps she hasn't realised how close to the boundary your conservatory is. She has every right to erect a fence on her land.

Welcome to GOY Traceygardenfence. I am not sure where you live in the UK but there are rules about how close to a neighbouring property one is allowed to build fences or erect sheds etc. SBG is right in advising you to talk to the neighbour first. Some of us have experience of neighbours from hell and it would be great if you can come to some arrangement with them so that you keep on at least speaking terms. If the fence is on the boundary between the two properties it may be that your conservatory is too close to the boundary. What was there before? We are not legal experts on planning matters, just gardening enthusiasts who enjoy sharing our knowledge with others. We can offer sympathy and sometimes a different perspective on problems our members have. We will look forward to hearing how you resolve the problem.

Thanks unfortunately our neighbour said this conservatory was built right on the boundary and she had desputes with the previous owner so I'm not sure how I'll resolve this lol

If that large window is on the boundary then I would be very unhappy if I was your neighbour. Does the window have to be replaced e.g. is it rotten or do you just want to change it because it will be aesthetically more pleasing? If she is correct she would probably have a case to say you are robbing her of the right to privacy. If you had the house surveyed it should have come to the surveyors attention that there had been difficulties with the neighbour. Your best bet still seems to be to get her to agree to you removing and replacing the fence after your window has been changed. If you only recently bought the house it might be worth speaking to your mortgage lender if you have one, the solicitor who handled the purchase, or the surveyor. Bad relations with neighbours can be a costly and distressing business and neither of you seem to be at fault. Can you postpone the delivery of the window from your supplier if you explain the problem you are facing. A bit of time could give you time to come to an amicable arrangement with the neighbour. Your title deeds will show the boundaries of your property. I am so sorry to hear of this having been through something similar. I remember Sarah Beenie, on a home improvement programme, advised a couple who were faced with a similar problem to replace the clear glass with obscure glass. If you choose level 5 obscure glass you will not be able to see out or your neighbour to see in but it might persuade her remove the fence to enable you to clean the window. Have a chat to your supplier. Good luck.

I should think a well aimed hose pipe would be the easiest
way to clean the window.

I don't think its legal to have clear glass in a position that overlooks the neighbour so closely. If you have your replacement in frosted glass as the others suggest and have it so it will swivel so you can clean it from inside the conservatory that should solve both problems. Upstairs flats often have that style of window so your supplier should have no problem getting you one.
Sadly if the window is already on order you might have to shell out for the new opener design, sorry.

As your conservatory is built on the boundary you have no rights at all over anything outside it. I'm surprised the original owners got planning permission to have a window there at all.