Also note that English is not particularly widely spoken. German seems quite widely spoken though.
I only got one taxi whilst there and my Hungarian was limited to things like hello, please, thank you and managed to get the message across by showing the hotel address and the taxi driver wrote the fare on a piece of paper first so it was agreed in advance and we knew what we were paying. It was only a short hop across the river though from the main town in Pest to our hotel in Buda.
We found similar with the public transport system though we had the benefit of meeting local friends who explained how it all worked and what to get. It's a very simple ticket system but very few of the staff at the underground stations or on the buses or trams speak much English.
I'd recommend getting your hotel to arrange a taxi for you at a pre-agreed price. If others from the hotel are going, maybe you could club together to share a minibus for a cheaper fee.