No, there is no reason the United Kingdom should dollarize. The euro is on the rise and the American Dollar is not as reliable as it used to be. There is no need for them to dollarize and should be embracing the Euro more than the American Dollar and should stay that way.
The United Kingdom has no need to dollarize. If we're talking about switching to or basing on the United States currency called the Dollar, that's an extremely bad idea. The American currency isn't as stable or reliable as it once was. The combined economic power of the Euro is a much safer haven these days, and we should embrace that currency instead.