There is a very detailed set of guidance for what can and cannot be held, available from HMRC; it's chapter 7, p. 72 onwards. (The sections highlighted in pink are the 2014 revisions, which added certain types of shares)
Some exceptions that might be relevant are -
- not all shares qualify - it has to be traded on a recognised exchange, but it is sometimes possible to bring non-traded shares in if acquired through an employee share scheme.
- shares in co-operative societies and community benefit societies cannot be held in an ISA
- ISAs cannot be used for futures or options
- some types of "non-UCTIS" investment funds that have limited redemption are prohibited
- cash can only be held in sterling (with some small exceptions)
This means that, for example, you could not hold shares in an Indian-listed company. You could not invest in a crowdfunded business and hold those shares within an ISA. You could not buy American shares, sell them for dollars, and park the dollars in the ISA.
Looking at the list of things you are allowed to hold, however, it's worth noting that the ISA provider does not have to offer all of these options - so your specific ISA might be more restricted.
For example, a provider might offer an ISA in which you can only buy specific investment funds. They might offer an ISA in which you can buy all sorts of UK shares, but they don't support foreign exchanges. Or they might support you buying shares on a US exchange, but not a German one. They may not let you move employee-scheme shares into the ISA (because it's too much administrative hassle) even if they are legally able to be held. And so on...