Private residence relief: settled property: common intention constructive trusts: is there an express trust?
The first point to check when dealing with a claim that there is a constructive trust is whether the transfer of the property actually created an express trust. If there is an express trust there can be no constructive trust. An express statement of the beneficial interests in the conveyance or transfer will be decisive unless varied by the parties at a later date. In Goodman v Gallant  EWCA Civ 15 Lord Justice Slade says:
In a case where the legal estate in property is conveyed to two or more persons as joint tenants, but neither the conveyance nor any other written document contains any express declaration of trust concerning the beneficial interests in the property (as would be required for an express declaration of this nature by virtue of section 53(1) (b) of the Law of Property Act 1925), the way is open for persons claiming a beneficial interest in it or its proceeds of sale to rely on the doctrine of “resulting, implied or constructive trusts”: (see section 53(2) of the Law of Property Act 1925). In particular, in a case such as that, a person who claims to have contributed to the purchase price of property which stands in the name of himself and another can rely on the well known presumption of equity that a person who has contributed a share of the purchase price of property is entitled to a corresponding proportionate beneficial interest in the property by way of implied or resulting trust: (see, for example, Pettitt v Pettitt  AC.777 at pp. 813-814 per Lord Upjohn). If, however, the relevant conveyance contains an express declaration of trust which comprehensively declares the beneficial interests in the property or its proceeds of sale, there is no room for the application of the doctrine of resulting implied or constructive trusts unless and until the conveyance is set aside or rectified; until that event the declaration contained in the document speaks for itself.
Lady Hale makes the same point in paragraph 49 of her opinion in Stack v Dowden.
In the olden days, before registration of title on certain events, including a conveyance on sale, became compulsory all over England and Wales, conveyances of unregistered land into joint names would in practice declare the purchasers’ beneficial as well as their legal interests. No-one now doubts that such an express declaration of trust is conclusive unless varied by subsequent agreement or affected by proprietary estoppel: see Goodman v Gallant.
Land Registry form
The land registry form TR1 includes a declaration of trust box. It is not mandatory to complete this and it will not be completed if there is only one transferee. If it has been completed it will constitute an express trust and will be binding between the parties to the declaration. It would not prevent a claim by a third party that there is a constructive trust. But as explained in paragraph CG65423 below that involves establishing a common intention to share the beneficial ownership or create a beneficial interest. If the legal owner has declared a trust in favour of other persons that shows that there was no intention to create a trust in favour of the third party who claims such a trust.
For example, a husband and wife buy a house and complete the TR1 showing that they own the property as tenants in common in equal shares. They allow their daughter to live in the house rent-free but she has to maintain the property and pay for the property insurance. When the house is sold the parents claim that they held it on constructive trust for the daughter. The fact that they declared they held the property on trust for themselves is good evidence that they did not intend to hold in on trust for anyone else. A constructive trust would have to arise later as a result of a fresh agreement or some further act of detriment by the third party such as a very substantial contribution to improvements. Such a later agreement would be exceptional. See CG65424.