What sounds most harsh to a Russian ear is when foreigners pronounce middle "е", "я", "ё" the same way as in "yes", "yay", "yolk", etc. For example, they try to pronounce "принесёт" as "приньесьёт" and so on. There is no "ь" there, only soft sounding consonants and the following vowels are also slightly softer because of that. Speaking about English and British English, in particular, the intonation and rhythm greatly contribute to your sounding foreign. In English it is normal to speed up or slow down your speech on a micro scale to make word stresses occur at equal intervals. Which is not the case with Russian language. Russian is closer to Italian in this respect. It is more melodically oriented than rhythmically oriented, so to speak. Also, excessive aspiration and muscular tension is not good for you when you speak Russian. Unless you are agitated, of course.