The remedies for those who have been refused entry clearance (visas) under the Points Based System (PBS) are rather slight. There is in general no appeal under the immigration rules, a restriction achieved by a rather arcane legislative route: section 88A(1) of the Nationality Immigration and Asylum Act 2002 explains that a person may not appeal against refusal of entry clearance if the decision to refuse is taken on grounds which relate to a provision of immigration rules specified by Order of the Secretary of State. There is such an Order: for the Immigration, Asylum and Nationality Act 2006 (Commencement No 8 and Transitional and Saving Provisions) Order 2008 explains that this applies only to those immigration rules requiring consideration under a "Points Based System".
However there is a limited remedy by way of administrative review. You can find it, for example, at Annex 4 of the Policy Guidance on Students. Recently I have come across cases where the Entry Clearance Officers have refused visas to children of PBS Migrants, perhaps because of disputes as to whether the parent they wish to join truly has sole responsibility for their care, and then stated the right of appeal is a limited one. One wonders whether this can be right. For sure, there is a limited right of appeal in PBS cases, ie those applications set out in immigration rules 245AA-245ZD: but the rules for migration of children and other family members are at rule 319AA onwards . So they appear to be applications made by way of an immigration rule that references, but is not itself part of, the Points Based System. This may have real importance in some cases, as although there remains the human rights (and if ever relevant, the race discrimination) grounds of appeal (section 88A(2)(a)), these are provisions which in some cases offer a more complex target to hit than simply establishing the simple requirements of the immigration rules.