They were not at all close. They did not have an atomic bomb production program. They had a modest reactor research program. This has been popularly conflated into a "race for the bomb," with the Germans being close to obtaining it, but this is just a myth deployed for various ends (sometimes just for drama, sometimes for justifying the US development of the bomb). It would have taken years' more effort at a much larger scale than they did it to develop a bomb.

For more details, see this or this reply, or this section of the FAQ.