App or easiest way to order a taxi

This site lists English speaking taxi companies, phone numbers at the bottom of the page.  I do not know, however, if it is up to date.

http://www.budapestagent.com/taxi-in-budapest.html

Suppose it is too late to help you now but hope it worked out for you.
I will say to future taxi riders to be sure to get a quote for a ride BEFORE sitting inside the cab.
A few weeks back when I had family in town we wanted to take a short ride from the Octagon to the city park.
My HU speaking husband went to several taxi's that were just parked on the st. and asked how much they charged.
None of them were willing to take the fare, they said it was too short of a ride to lose their spot in line.
We all just thought , forget it and we decided to just walk, we had a run in on the subway with those odd agents and didn't want to go underground again.
Walked past one more cab and asked just once more how much.
The young driver gave us a good rate and took the 4 of us to the park.
My husband asked him in Hungarian why those other 3 or so drivers had refused a fare when they could possibly be sitting for hours waiting for a ride.
He said he was sort of a new driver and not 100% sure but he thought they had "other business" then actually driving people.
Ok, makes my mind wonder...
My husband was a taxi driver here in Budapest in the late 1960's when he was a young man.
He just doesn't understand how they operate these days, totally unprofessional in so many ways now.