It looks like there's close on unanimity from those that have used that type of service: again, yes. Having stuff packed for you is the only way to fly.
It is interesting how many small family businesses exist in that category, or at least, back in the day when I was running my own IT business and developed an unintentional vertical market in removal companies through recommendation. I suspect that while some may have disappeared, many remain as attested to by the vans you see.
What I learned, which will come as no surprise, is that not all companies are the same, a minority are best avoided. You might think, "no shit, Sherlock" but when you consider the nature of the business is to provide a one-off service, it takes the responsibility and consideration you can find in a small family company to maintain a high level of service. True, the Internet has changed much since then but the choices are likely to remain the same, especially since so often it comes down to calling around to find a company with availability. Either pay a premium and go for one of the big companies, or identify a small company with a good reputation ideally through personal recommendation, but possibly through review sites.
I was able to avail myself of insider knowledge when Mrs Ham & I moved to Ham Hall, 23 years ago. Somewhat amusingly the chosen removal company we used underestimated the amount of crap two people in two 2-bed flats+ 2 garages could accumulate. (ans: 1.75 pantechnicons), but performed the service with good humour, none the less.