You need to discuss this with your solicitor. If he is secretly buying a property, he is disposing of assets (ie. cash) and acquiring hidden assets (the secret property).
Have a look at this:
www.divorce.co.uk/your-finances/hidden-assets-on-divorce
If you think your spouse may try to dispose of assets, you need to act quickly. Take legal help straight away and act decisively. The courts can intervene in three basic ways:
An order under section 37 of the Matrimonial Causes Act 1973 - there are two types of order under this provision. First, an order preventing the disposal of assets that might be about to take place and which would prejudice the applicant. Secondly, an order requiring assets that have already been disposed of to be transferred back.
The freezing order - this is very similar to the first type of section 37 order but has wider application in that it prevents the disposal of assets. However, the powers of the court with a freezing order are more extensive: they extend to assets abroad and prevention of the disposal of assets that have not actually come into existence yet, for example a pension that is about to be paid out.
Search orders (previously known as Anton Pillar orders) – used rarely, but can be extremely effective in getting information about assets that have been hidden. They are very expensive to get and implement and are likely to be appropriate only in cases involving very serious non-disclosure and where there is a lot of money at stake
In practical terms, if he is in the process of buying a property he will need to be "doing certain things" - ie. having contact with a conveyancing solicitor, speaking to the bank etc. You could try sleuthing around his phone to see what numbers he is calling and see if any of them are solicitors.
If he is going to view properties, then old fashioned following him may help flush it out.
If he has bought it already, he will need to set up DD for payment of mortgage (assuming not full cash buy) and utilities - so does he have a secret bank account?
There are limits to what you can get yourself and even if you do, what is admissible in court. Running off with his laptop is unlawful and won't help. Speak to a specialist divorce lawyer with experience of asset concealment.
The last bit is important - this isn't just bog standard high street firm stuff. High net worth divorces can get very nasty. As you would expect, aggressive intelligent high earning men are no fools and can quite easily hide stuff. You need lawyers who have seen these kind of tricks before and know how to go about dealing with it.