Under both US and UK law the first question is whether the extent of reproduction would (absent permission) amount to infringment. This is a question of substantiality of reproduction. However US law contains a defence of parody, which UK law does not.

Next question, is the first work in copyright? This can be a very very vexed question, and subject to wholly different concerns in the UK and USA. In both if the author has been dead for over 70 years the work will almost inevitably be out of copyright, but in the UK there were some categories of perpetual copyright that only became time limited in 1988 and may run until 2038. In the USA the duration of copyright in old works may have been shorter thanks to the old US 28 years + 28 years under the 1909 US Copyright Act, and US works may also have lost copyright due to non-renewal during that and the later 28 + 75 year structure, although works of non-US Berne Convention origin may have returned to US copyright after the US Berne COnvention Implimentation Act.

Third question - is the relevant act restricted by copyright. The USA has a "private use" doctrine. The UK does not. So in the UK if permission is needed and not obtained the mere writing (in a material form) of the new work will infringe copyright in the old, no matter how private the reproduction is kept. This is often overlooked by Americans.

Fourth question - who owns the relevant part of copyright. Copyright has always been divisible in the UK, whereas under the US 1909 Act some argued that copyright was indivisible and that all that could be transferred were "rights under copyright" but that pedantry is no longer with us. A publisher may have taken an assignment of the whole of the copyright - or not. But for old works the title to the US "renewal term" need not necessarily have vested in the author, but if he was dead could have gone to a member of family. There is much learning in the USA around this topic, the leading case being "Rear Window". As the US law now stands, the doctrine around this has largely been replaced by two separate rights of termination - one for old works, one for newer. Even in the UK, there maybe a reversionary right for works that were first assigned before 1956 - they may be affected by the proviso to S. 5(2) of the Copyright Act 1911 and revert to the author's estate 25 years after his death.

Have fun.