Hi Neil
As John says if it's a loose business relationship then there shouldn't be too many problems. In a similar way I've worked on jobs with Clinton and others but it's usually because the size of the job demands it. In this type of situation the job usually "belongs" to one of you and in effect you're subbing out part of the work. If both of you are doing this then there is less chance of resentment from either party.
In a partnership agreement-and do be very careful over this, because even if there is nothing written down-whilst all is going swimmingly there are rarely any problems. When problems do occur if can be the case that one party would argue that by dint of the situation a partnership had been formed and therefore the parties would be estopped from denying it. It only takes for one party of the partnership to feel grieved that they are putting more into the relationship for the whole ship to go belly up.
If it's to be more than a loose, occasional joint working then you need to cover such matters as who does what, what each of you is bringing to the relationship, and what is expected of each party and what the split of the rewards are to be. So for example, one person may be brilliant at bringing in the business which can be perceived as less back-breaking, and have rubbish equipment/cleaning skills, whilst the other partner has all the equipment and technique (and has to work long unsociable hours actually doing the cleaning) but couldn't give away a beer in a pub. In such a scenario you could have a perfect storm of resentment building up as to which party makes the partnership work best.
(Another example would be Rolls Royce cars. Mr Royce was a brillian engineer/mechanic whilst Mr Rolls was the master of selling exclusive cars. Thankfully they worked out their differences including the fact that the cars are called Rolls Royces and not Royce Rolls (although it is also known that within the factories they are always known just by the name "Royces". But I digress.)
A formal "partnership agreement" whilst it will cost you money to draw up can save hours of arguements, lawyers bills and generally "losing out" in the long run. And such an agreement is really no different (and probably cheaper) than setting up a limited company with the accompanying Memorandum and Articles of Association which are in effect the same thing as a Partnership Agreement.
Rog