You almost certainly need to change the LNB - the bit in front of the dish. Sky Q uses a wideband LNB that can pick up all frequencies on either the horizontally polarized or all frequencies on the vertically polarized frequencies, so just needs two connexions to permanently receive all channels, which allows it to record or display numerous channels at once.
Most Freesat receivers, including TVs, need an older style LNB that doesn't cover all the frequency range without switching - and was actually the sort originally used by Sky+.
This sounds to me like the most likely culprit, if your dish has a Sky Q or other incompatible LNB on it. I know Sky were using quad LNBs for a while (My partner at the time had to have one installed on his) though I don't know how those work beyond being able to supply two separate tuned signals at once for Sky+ functionality. I was also going to ask if dishes angled for Sky/Sky+/Sky Q need to be readjusted to pick up FreeSat. I'm going to guess they don't come from the
same satellite (Sky/Comcast play
nicely with competitors?!

) so if the FreeSat satellite is in a different location (Particularly at a different azimuth/angle) you might need to adjust the pitch of your dish.
A quick test - If you still have your Sky+ box - Is to plug that in to the satellite connection and see if that still gets full Sky signal. If so then it shows the dish is in the correct position for
Sky satellites, and you might need to investigate whether the dish requires adjustment. (With Sky/Comcast and their owner being as they are, their having bought "exclusive" orbital positions for their satellites wouldn't surprise me in the slightest. It'd mean competitors are forced onto different orbits thus received on a different azimuth.)
When I got a FreeSat dish to go with my LG TV (after old aerial damaged in a storm) the installer said that I’ve to get rid of a large tree that was in a ‘direct line’. Much work with a saw later, everything seems to be fine.
I really hope you checked the tree didn't have a TPO disc on it before you did that! Those things can appear out of nowhere (We have a tree in my garden that took root around the time I moved in; It "sprouted" a TPO disc four years ago) and can land you in a
lot of trouble over unauthorised adjustments to them!
But yes, a clear line-of-sight is necessary for satellite dishes - The signals are so weak by the time they enter Earths atmosphere they can be stopped by something as thin as toilet paper. Crazy to think that floating past the transmitting end of that signal would result in instant vaporisation; The power output is
almost as strong as a TGV with the power controller on 8%!
